24 Jan Aurélien Sagnier EP-Palaiseau "An arithmetic site of Connes-Consani type for the Gaussian integers" 31 Jan Jozsef Beck Rutgers "An annoying question about eigenvalues" 7 Feb Lev Borisov Rutgers "Equations of Cartwright-Steger surface" 21 Feb Dhruv Ranganathan MIT "Curves, maps, and singularities in genus one" 28 Feb Rohini Ramadas Harvard "Algebraic dynamics from topological and holomorphic dynamics" 7 Mar CANCELLED DUE TO SNOW 15 Mar Nicola Pagani U.Liverpool "The indeterminacy of universal Abel-Jacobi sections" 21 Mar CANCELLED DUE TO SNOW 28 Mar Ana-Maria Castravet Northeastern U. "Derived categories of moduli spaces of stable rational curves" 4 Apr CANCELLED DUE TO SNOW 11 Apr Chiara Damiolini Rutgers "Conformal blocks attached to twisted groups" 18 Apr Joe Waldron Princeton "Singularities of general fibers in positive characteristic" 2 May Ben Bakker U. Georgia "Hodge theory and o-minimal geometry" 9 May Antonella Grassi U. Penn "Singularities in geometry, topology and strings" (in H705)Classes end Monday, April 30; Final Exams are May 4-9, 2018
13 Sep Louis Rowen Bar-Ilan Univ "A general algebraic structure theory for tropical mathematics" 20 Sep Nicola Tarasca Rutgers "K-classes of Brill-Noether loci and a determinantal formula" 27 Sep Pham Huu Tiep Rutgers "Character levels and character bounds" 4 Oct Dave Jensen Yale "Linear Systems on General Curves of Fixed Gonality" 11 Oct Gernot Stroth Martin-Luther Univ. "On the Thompson Subgroup" 18 Oct Han-Bom Moon IAS "Birational geometry of moduli spaces of parabolic bundles" 1 Nov Danny Krashen Rutgers "Extremely indecomposable division algebras" 8 Nov Lev Borisov Rutgers "Explicit equations of a fake projective plane" 15 Nov Julia Hartmann U. Penn. "Local-global principles for rational points and zero-cycles" 22 Nov --- no seminar --- Thanksgiving is Nov. 23; Friday class schedule 29 Nov Chuck Weibel Rutgers "K-theory of line bundles and smooth varieties" 6 Dec Seth Baldwin N.Carolina "Equivariant K-theory associated to Kac-Moody groups" 13 Dec Brooke Ullery Harvard "Gonality of complete intersection curves" Classes end December 13; Final Exams are December 15-22, 2017Spring 2017 Seminars (Wednesdays at 2:00 in H705) 22 Feb Ryan Shifler Virginia Tech "Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian" 1 Mar Chuck Weibel Rutgers "The Witt group of surfaces and 3-folds" 8 Mar Oliver Pechenik Rutgers "Decompositions of Grothendieck polynomials" 15 Mar no seminar ------------------- Spring Break ---------- 22 Mar Ilya Kapovich UIUC/Hunter College "Dynamics and polynomial invariants for free-by-cyclic groups" 29 Mar Rachel Levanger Rutgers "Interleaved persistence modules and applications of persistent homology to problems in fluid dynamics" 5 Apr Cristian Lenart Albany-SUNY "Kirillov-Reshetikhin modules and Macdonald polynomials: a survey and applications" 19 Apr Anders Buch Rutgers "Puzzles in quantum Schubert calculus" 26 Apr Sjuvon Chung Rutgers "Equivariant quantum K-theory of projective space"Classes end May 1; Final Exams are May 4-10, 2017
Fall 2016 Seminars (Wednesdays at 2:00 in H423) 21 Sept Fei Qi Rutgers "What is a meromorphic open string vertex algebra?" 28 Sept Zhuohui Zhang Rutgers "Quaternionic Discrete Series" 5 Oct Sjuvon Chung Rutgers "Euler characteristics in cominuscule quantum K-theory" 12 Oct Ed Karasiewicz Rutgers "Elliptic Curves and Modular Forms" 19 Oct Natalie Hobson U.Georgia "Quantum Kostka and the rank one problem for sl2m" 26 Oct Oliver Pechenik Rutgers "K-theoretic Schubert calculus" 2 Nov Vasily Dolgushev Temple U "The Intricate Maze of Graph Complexes" 9 Nov Jason McCullough Rider U. "Rees-like Algebras and the Eisenbud-Goto Conjecture" 16 Nov Robert Laugwitz Rutgers "Representations of p-DG 2-categories" 23 Nov --- no seminar --- Thanksgiving is Nov. 24; Friday class schedule 30 Nov Semeon Artamonov Rutgers "Double Gerstenhaber algebras of noncommutative poly-vector fields" 7 Dec Daniel Krashen U.Georgia "Geometry and the arithmetic of algebraic structures" (Special talk) 14 Dec Angela Gibney U.Georgia "Vector bundles of conformal blocks on the moduli space of curves" (Special talk) Classes end December 14; Final Exams are December 16-23, 2016
Spring 2016 Seminars (Wednesdays at 2:00 in H705) 20 Jan Louis Rowen Bar-Ilan Univ "Symmetrization in tropical algebra" 3 Feb Volodia Retakh Rutgers "Generalized adjoint actions" 10 Feb Omer Bobrowski Duke (@noon!) "Random Topology and its Applications" 17 Feb Lisa Carbone Rutgers "Arithmetic constructions of hyperbolic Kac-Moody groups" 2 Mar Chuck Weibel Rutgers "Relative Cartier divisors" 9 Mar Lev Borisov Rutgers "Elliptic genera of singular varieties and related topics" 16 Mar no seminar ------------------- Spring Break ---------- 23 Mar Rachel Levanger Rutgers "Auslander-Reiten quivers of finite-dimensional algebras" 30 Mar Richard Lyons Rutgers "Aspects of the Classification of simple groups" 6 Apr Richard Lyons Rutgers "Aspects of the Classification, continued" 13 Apr Siddhartha Sahi Rutgers "Eigenvalues of generalized Capelli operators" 20 Apr Ed Karasiewicz Rutgers "Some Aspects of p-adic Representations & the Casselman-Shalika Formula" 27 Apr Semeon Artamonov Rutgers "Noncommutative Poisson Geometry" Classes end May 2; Final Exams are May 4-10
Fall 2015 Seminars (Wednesdays at 2:00 in H425) 7 Oct Chuck Weibel Rutgers "Monoids, monoid rings and monoid schemes" 14 Oct Lev Borisov Rutgers "Introduction to A-D-E singularities" 21 Oct Dylan Allegretti Yale "Quantization of Fock and Goncharov's canonical basis" 28 Oct Volodia Retakh Rutgers "Noncommutative Cross Ratios" 4 Nov Gabriele Nebe U.Aachen "Automorphisms of extremal codes" 11 Nov Chuck Weibel Rutgers "Relative Cartier divisors and polynomials" 18 Nov Glen Wilson Rutgers "Motivic stable homotopy over finite fields" 25 Nov --- no seminar --- Thanksgiving is Nov. 26; Friday class schedule 2 Dec Anders Buch Rutgers "The Thom Porteous formula" 9 Dec Pham Huu Tiep U. Arizona "Representations of finite groups and applications " Classes end Dec. 10; Final Exams are December 15-22
Spring 2015 Seminars (Wednesdays at 2:00 in H124) 27 Jan --- 4 Feb Jesse Wolfson Chicago "The Index Map and Reciprocity Laws for Contou-Carrère Symbols" 18 Feb Justin Lynd Rutgers "Fusion systems and centric linking systems" 25 Feb Lev Borisov Rutgers "Zero divisors in the Grothendieck ring of varieties" 4 Mar Volodia Retakh Rutgers "Noncommutative triangulations and the Laurent phenomenon" 6 MarC Burt Totaro UCLA/IAS "Birational geometry and algebraic cycles" (Colloquium) 11 Mar Anders Buch Rutgers "TK" 18 Mar no seminar ------------------- Spring Break ------------------ 22 Apr Howard Neuer Rutgers "On special cubic 4-folds" Classes end May 4; Spring Final Exams are May 7-13
Fall 2014 Seminars (Wednesdays, 3:15-4:15PM in H525) 17 Sep Edwin Beggs U.Swansea "Semiclassical approximation to noncommutative Riemannian geometry" 24 Sep Anders Buch Rutgers "Equivariant quantum cohomology and puzzles" 8 Oct Lev Borisov Rutgers "Cut and paste approaches to rationality of cubic fourfolds" 15 Oct Chuck Weibel Rutgers "The Witt group of real varieties" 22 Oct Ed Karasiewicz Rutgers "Jacobians of modular curves" 29 Oct Charlie Siegel (IPMU Japan) "A Modular Operad of Embedded Curves" 5 Nov no seminar 12 Nov Marvin Tretkoff Texas A&M "Some non-compact Riemann surfaces branched over three points" 19 Nov Ashley Rall U. Virginia "Property T for Kac-Moody groups" 26 Nov (Thanksgiving is Nov. 27) no seminar 3 Dec Alex Lubotzky NYU/Hebrew U. (Israel) "Sieve methods in group theory"
Spring 2014 Seminars (Wednesdays at 2:00 in H124) Apr 26 Anatoly Vershik, St. Petersburg State University, Russia "Invariant measures and standardness" Mar 5 Greg Muller, Michigan "Locally acyclic cluster algebras" Mar 12 Julianne Rainbolt, Saint Louis University "Bruhat cells which contain only regular elements" Mar 26 Bianca Viray, Brown U "Unramified Brauer classes on cyclic covers of the projective plane" Apr 9 Lev Borisov, Rutgers "An annoying problem in toric geometry" Apr 23 Howard Nuer, Rutgers "An introduction to cubic fourfolds and their moduli space" Apr 30 Vijay Ravikumar, Tata Institute "Equivariant Pieri rules for Isotropic Grassmannians"
Fall 2013 Seminars (Wednesdays at 2:00 in H525) Details for Fall 2013 seminars are located at THIS SITE4 Sep Delaram Kahrobaei CUNY "Applications of Algebra in Information Security" 2 Oct Bob Guralnick USC and IAS "Dimensions of Fixed Spaces" 9 Oct Leonid Petrov Northeastern "Robinson-Schensted-Knuth correspondences and their $(q,t)$-deformations" 16 Oct Knight Fu Rutgers "Torsion Theory and Slice Filtration of Homotopy Invariant Sheaves With Transfers" 23 Oct Ralph Kaufmann Purdue/IAS "Three Hopf algebras and their common algebraic and categorical background" 30 Oct Howard Nuer Rutgers "Bridgeland Stability and Moduli on Enriques Surfaces" 6 Nov Andrew Blumberg U.Texas "Probabilistic inference in topological data analysis" 13 Nov Pierre Cartier IHES "Galois groups of differential equations: a noncommutative analog" 20 Nov Zsolt Patakfalvi Princeton "Classification of algebraic varieties: classical results and recent advances in positive characteristic"
Spring 2013 Seminars (Wednesdays at 2:00 in H525) 24 Jan Daniel Erman Michigan "Equations, syzygies, and vector bundles" 30 Jan David Anderson U. Paris "Equivariant Schubert calculus: positivity, formulas, applications" 6 Feb Chuck Weibel Rutgers "What is a Derivator?" 13 Feb V. Retakh Rutgers "A geometric approach to noncommutative Laurent phenomenon" 20 Feb Tatiana Bandman Bar-Ilan "Dynamics and surjectivity of some
word maps on SL(2,q)" 27 Feb Bob Guralnick USC and IAS "Strongly Dense Subgroups of Algebraic Groups" 13 Mar Mina Teicher Bar-Ilan "The 3 main problems in the braid group" 20 Mar no seminar -------------- Spring Break ------------- 3 Apr Joe Ross USC "Intersection theory on singular varieties" 10 Apr Lev Borisov Rutgers "Hilbert modular threefolds of discriminant 49" 17 Apr Charlie Siegel (IPMU Japan) "Cyclic Covers, Prym Varieties and the Schottky-Jung Relations" 24 Apr Freya Pritchard CUNY "Implicit systems of differential equations" 1 May Alexei Stepanov (St.Petersburg State University) "Structure of Chevalley groups over rings"
Fall 2012 Seminars (Wednesdays at 2:00 in H525) 19 Sept Chuck Weibel Rutgers "Binary codes and Galois covers of varieties" 10 Oct Anders Buch Rutgers "Curve neighborhoods" 17 Oct Dan Grayson IAS "Computations in intersection theory" 24 Oct Justin Lynd Rutgers "Fusion systems with prescribed involution centralizers" 31 Oct Lev Borisov Rutgers "On Hilbert modular threefolds of discriminant 49" 7 Nov Oliver Rondigs Osnabruck, Germany "On the slice filtration for hermitian K-theory" 14 Nov Howie Nuer Rutgers "surfaces on Calabi-Yao 3-folds" 21 Nov no seminar, Friday classes (Thanksgiving week) 28 Nov Susan Durst Rutgers "Universal labelling algebras for directed graphs" 5 Dec Anastasia Stavrova U.Essen "Injectivity property of etale H^1, non-stable K_1, and other functors" 12 Dec Joe Ross USC "Presheaves with oriented weak transfers"Fall 2012 Semester starts Sept.4; (Wednesday Nov. 21 will be Friday classes).
Classes end Wed., Dec. 12; Final Exams start Friday 12/14/11
Spring 2012 Seminars (Wednesdays at 2:00 in H525) 25 Jan Vasily Dolgashev Temple Univ. "Exhausting quantization procedures" 8 Feb Chuck Weibel Rutgers "Shift Equivalence and Z[t]-modules" 15 Feb Pablo Pelaez Rutgers "An introduction to weights" 22 Feb Anders Buch Rutgers "K-theory of miniscule varieties" 29 Feb Julia Plavnik U.Cordoba "From algebra to category theory: a first approach to fusion categories" 7 Mar Anastasia Stavrova U.Essen "On the unstable K_1-functors associated to simple algebraic groups" 14 Mar no seminar -------------- Spring Break ------------- 21 Mar Mark Walker U. Nebraska "Invariants of Matrix Factorizations" 28 Mar Lev Borisov Rutgers "Combinatorial aspects of toric mirror symmetry" 5 Apr Joe Ross USC "Cohomology Theories with Supports" Thursday 11:00AM in Hill 425 11 Apr V. Retakh Rutgers "Noncommutative Laurent Phenomena" 18 Apr Ben Wyser U.Georgia "Symmetric subgroup orbit closures on flag varieties as universal degeneracy loci" 25 Apr Ling Bao Chalmers U. (Sweden) "Algebraic symmetries in supergravity"Spring 2012 Semester starts Jan. 17, Classes end April 30,
Spring Break is March 11-18, Exams start May 3.
Fall 2011 Seminars (Wednesdays at 2:00PM in H423) 14 Sept Charles Siegel U. Penn. "The Schottky Problem and genus 5 curves" 28 Sept Abid Ali Rutgers "Congruence subgrous of lattices in rank 2 Kac-Moody groups over finite fields" 5 Oct Raika Dehy Cergy-Pontoise "Cluster algebras and categorification" 12 Oct Chuck Weibel Rutgers "What (besides varieties) are motivic spaces?" 19 Oct Raika Dehy Cergy-Pontoise "Cluster algebras and categorification (bis)" 26 Oct Anders Buch Rutgers "Giambelli formulas for orthogonal Grassmannians" 2 Nov Alice Rizzardo Columbia "On Fourier-Mukai type functors" 9 Nov Changlong Zhong Ottowa "Comparison of Dualizing Complexes" 16 Nov Anastasia Stavrova U.Essen "The Serre-Grothendieck conjecture on torsors and the classification of simple algebraic groups" 23 Nov no seminar, no classes (Thanksgiving week) 30 Nov Lev Borisov Rutgers "Elliptic functions and equations of modular curves" 7 Dec Pablo Pelaez Rutgers "Homotopical Methods in Algebraic Geometry"Fall 2011 Semester starts Sept.1; (Thursday Sept.8 will be Monday classes).
Classes end Tues, Dec. 13; Final Exams start Friday 12/16/11
Spring 2011 Seminars
(Wednesdays at 2 PM in CoRE 431)21 Jan Chenyang Xu Princeton Colloquium talk (Friday) 26 Jan Grigor Sargsyan UCLA TBA (Monday Jan. 24) 28 Jan Ivan Losev MIT Colloquium talk (Friday) 4 Feb A. Salehi Golsefidy Princeton Colloquium talk (Friday) 9 Feb Louis Rowen Bar Ilan U. "Tropical Algebra" 16 Feb no seminar 23 Feb Christian Haesemeyer UCLA "Rational points, zero cycles of degree one, and A^1-homotopy theory" 2 Mar Volodia Retakh Rutgers "Linear recursive sequences, Laurent phenomenon and Dynkin diagrams" 9 Mar Chuck Weibel Rutgers "Monoid algebras and monoid schemes" 16 Mar no seminar -------------- Spring Break ------------- 30 Mar Volodia Retakh Rutgers "Hilbert series of algebras associated to direct graphs and order homology" 6 Apr Lev Borisov Rutgers "Syzygies of binomial ideals and toric Eisenbud-Goto conjecture" 13 Apr Crichton Ogle Ohio State "Cyclic homology, simplicial rapid decay algebras, and applications to K*t(l¹(G))" 20 Apr Susan Durst Rutgers "Twisted Polynomial Rings and Embeddings of the Free Algebra" 27 Apr Chuck Weibel Rutgers "Derived categories of graded modules" 4 May Spring Finals are May 5-11; last day of classes is May 2 (Monday)
Fall 2010 Seminars (Mondays at 4:30PM in H705) 20 Sept Uma Iyer Bronx Community College "Quantum differential operators" (4:50 PM) 27 Sept Chuck Weibel Rutgers "Monoids and algebraic geometry" (4:50 PM) 4 Oct Bob Guralnick USC "Dimensions of fixed point spaces of elements in linear groups" (4:50 PM) 11 Oct Volodia Retakh Rutgers "Hilbert series of algebras associated to directed graphs and order homology" (4:50 PM) 18 Oct Lev Borisov Rutgers "The Pfaffian-Grassmannian derived equivalence" (4:30 PM) 1 Nov Chuck Weibel Rutgers "etale cohomology operations" (4:30 PM) 8 Nov Anders Buch Rutgers "Pieri rules for the K-theory of cominuscule Grassmannians" (4:30 PM) 15 Nov Volodia Retakh Rutgers "A short proof of the Kontsevich cluster conjecture" (4:30 PM) 22 Nov no seminar (Wednesday class schedule, Thanksgiving week) 29 Nov Earl Taft Rutgers "The Lie product in the continuous Lie dual of the Witt algebra" (4:30 PM) 6 Dec Chuck Weibel Rutgers "Motivic cohomology operations" (4:30 PM) 13 Dec Ralph Kaufmann Purdue&IAS "Algebraic Structures from Operads" (4:30 PM) Fall Finals are Dec. 16-23; last day of classes is Dec 13 (Monday)
Spring 2010 Seminars (Mondays at 4:50 in H705) 1 Feb Max Karoubi Univ. Paris 7 "Periodicity in Hermitian K-groups" 15 Feb Chuck Weibel Rutgers Exceptional objects (after Polishchuk) 22 Feb 1 Mar Ray Hoobler CCNY "Applications of stable bundles to Witt groups and Brauer groups" 8 Mar Christian Kassel CNRS & U.Strasbourg "Drinfeld twists and finite groups" 15 Mar no seminar -------------- Spring Break ------------- 22 Mar Earl Taft Rutgers "Hopf algebras and recursive sequences" 29 Mar Chuck Weibel Rutgers "Tilting 1" 5 Apr Carlo Mazza U. Genoa "The K-theory of motives" 12 Apr Miodrag Iovanov USC "Generalized Frobenius algebras, Integrals and applications to Hopf algebras and compact groups" 19 Apr Chuck Weibel Rutgers "Tilting 2" 26 Apr Robert Wilson Rutgers "Tilting 3 " 3 May William Keigher Rutgers-Newark "Module Structures on the Ring of Hurwitz Series" Spring Break is March 13-21, 2010; Final Exams begin Thursday May 6.
28 Sep no seminar Yom Kippur 5 Oct Lourdes Juan Texas Tech Differential Central Simple Algebras and Picard-Vessiot representations 12 Oct Bob Guralnick USC Derangements in Finite and Algebraic Groups 19 Oct Ken Johnson Penn State-Abington Mathematics arising from a new look at the Dedekind-Frobenius group matrix and group determinant 2 Nov Chloe Perin Hebrew Univ. "Induced definable structure on cyclic subgroups of the free group" 9 Nov Paul Ellis U. Connecticut "The classfication problem for finite rank dimension groups" 16 Nov Ravi Srinivasan RU-Newark "Picard-Vessiot Theory" 23 Nov Vladimir Retakh Rutgers "Noncommutative algebra and combinatorial topology" 30 Nov Chuck Weibel Rutgers "homotopy model structures as tools for homogical algebra" 7 Dec no seminar cancelled due to Gelfand Memorial Fall 2009 Semester begins Tuesday Sept 1; Labor Day is Sept. 7 Final Exams begin Wednesday Dec 16, 2009; Math Group Exams are Dec. 16 (4-7PM).
2 Feb: Chuck Weibel Rutgers "Stability conditions for triangulated categories" 9 Feb: Luis Caffarelli U. Texas Special Colloquium talk at this time 16 Feb: Vladimir Retakh Rutgers "Lie algebras over noncommutative rings" 23 Feb: Leon Pritchard CUNY "Partitioned differential quasifields" 2 Mar: Jan Manschot Rutgers-Physics "Stability conditions in physics" 16 Mar no seminar -------------- Spring Break ------------- 30 Mar: Elizabeth Gasparim Edinburgh "The Nekrasov Conjecture for Toric Surfaces" 6 Apr: Vladimir Retakh Rutgers "Noncommutative Laurent phenomenon" 13 Apr: Bill Keigher Rutgers-Newark "Differential quasifields" 20 Apr: Chris Woodward Rutgers "Morphisms of cohomological field theories and behavior of Gromov-Witten invariants under quotients" 27 Apr: Gregory Ginot Univ.Paris "higher order Hochschild (co)homology"
Spring Break is March 14-22, 2009; Final Exams begin Thursday May 7.
5 Sep:# Paul Baum Penn State "Morita Equivalence Revisited" Talk is Friday at 2PM in H705 15 Sep: no seminar MSMF Reception 18 Sep: Vasily Dolgushev UC Riverside "Formality theorems for Hochschild (co)chains and their applications" Talk at 2PM in H425 22 Sep: Mike Zieve Rutgers "Rationality and integrality in dynamical systems" 29 Sep no seminar Rosh Hoshanna 6 Oct: Chuck Weibel Rutgers "The de Rham-Witt complex of R[t]" 13 Oct: Anders Buch Rutgers "Quantum K-theory" 20 Oct: Earl Taft Rutgers "Combinatorial Identities and Hopf Algebras" 27 Oct: Siddhartha Sahi Rutgers "Interpolation and binomial identities in several variables" 3 Nov: Leigh Cobbs Rutgers "Infinite towers of co-compact lattices in Kac-Moody groups" 10 Nov: Jarden Logic Seminar "The absolute Galois group of subfields of the field of totally S-adic numbers" 14 Nov: Guillermo Cortiñas Buenos Aires "K-theory of some algebras associated to quivers" Talk is Friday at 2PM in H425 17 Nov no seminar ------- ------------------------------ 24 Nov: Robert Wilson Rutgers "Splitting Algebras associated to cell complexes" 1 Dec: Roozbeh Hazrat Queens Univ. Belfast "Reduced K-theory of Azumaya algebras" 9 Dec: Steven Duplij Kharkov Univ. "Quantum Enveloping Algebras and the Pierce Decomposition " Talk is Tuesday, 2PM in H425 Fall 2008 Semester begins Tuesday Sept 2; Final Exams begin Monday Dec 15, 2008.
25 Jan(F) W. Vasconcelos Rutgers The Chern numbers of a local ring (I) 28 Jan: Vladimir Retakh Rutgers "Obstructions to formality and obstructions to deformations" 4 Feb: Chuck Weibel Rutgers "Generation of Galois cohomology by symbols" 5 Feb(T)* Tony Milas SUNY Albany "W-algebras, quantum groups and combinatorial identities" 8 Feb(F) M. Zieve Rutgers "The lattice of subfields of K(x) 11 Feb: Zin Arai Kyoto Univ "Complex dynamics and shift automorphism groups" 18 Feb: Andrzej Zuk Univ Paris "Automata Groups" 25 Feb: Mike Zieve Rutgers "Automorphism groups of curves" 29 Feb(F) Laura Ghezzi CUNY "Generalizations of the Strong Castelnuovo Lemma" 3 Mar: Chuck Weibel Rutgers "Model categories versus derived categories" 10 Mar: R Parimala Emory Univ. "Rational points on homogeneous spaces" 14 Mar#* Tom Robinson Rutgers "Formal differential representations" 11:55 AM Friday in Hill 425 17 Mar: no seminar -------------- Spring Break ------------- 28 Mar#* David Ben-Zvi IAS & U.Texas "Real Groups and Topological Field Theory" 28 Mar(F) Jooyoun Hong Purdue "Homology and Elimination" 31 Mar: Siddhartha Sahi Rutgers "Tensor categories and equivariant cohomology" 4 Apr(C) David Saltman CCR and U.Texas "Division Algebras over Surfaces" 7 Apr: Earl Taft Rutgers "The boson-fermion correspondence and one-sided quantum groups 14 Apr: Colleen Duffy Rutgers "Graded traces and irreducible representations of graph algebras" 21 Apr: Semyon Alesker Tel-Aviv U. "Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets" 28 Apr: Jim Borger Australia Natl Univ. "Witt vectors, Lambda-rings, and absolute algebraic geometry" 5 May: Richard Lyons Rutgers "Subgroups of Algebraic Groups and Finite Groups" Spring 2008 Semester begins Tuesday Jan 22; Spring Finals are May 8-14, 2008
7 Sep* Benjamin Doyon Durham Conformal field theory and Schramm-Loewner evolution 14 Sep* Liang Kong Max Planck An introduction to open-closed conformal field theory 28 Sep Richard Lyons Rutgers Presidential Address and Department Reception 5 Oct Diane Maclagan Rutgers-Warwick Starts at 2:15! "Equations for Chow and Hilbert quotients" 12 Oct Rafael Villareal IPN,Mexico "Unmixed clutters with a perfect matching" 19 Oct POSTPONED to November 16 2 Nov# Andrea Miller Harvard POSTPONED 9 Nov Dan Krashen U. Penn Starts at 2:20!Patching subfields of division algebras 16 Nov Angela Gibney U. Penn A new candidate for the nef cone of M0,n 23 Nov Tom Turkey Plymouth Colony ---------Thanksgiving Break----------- 3 Dec: Dirk Kreimer IHES (France) Monday at 4:40! Hopf and Lie algebras for renormalizable quantum field theories 7 Dec V. Retakh Rutgers date(s) to change TK Fall Classes began September 4, 2007; Final Exams began Friday, Dec 14, 2007.
22 Sep: Corina Calinescu OSU Intertwining vertex operators and combinatorial representation theory 8 Dec* Haisheng Li RU-Camden Certain generalizations of twisted affine Lie algebras and vertex algebras 30 Mar* Bill Cook Rutgers Vertex operator algebras and recurrence relations 6 Apr* Antun Milas SUNY-Albany On a certain family of W-algebras 13 Apr* Vincent Graziano SUNY-Stony Brook G-equvariant modular categories and Verlinde formula 20 Apr* Corina Calinescu OSU Vertex-algebraic structure of certain modules for affine Lie algebras underlying recursions 27 Apr* Tom Robinson Rutgers A Formal Variable Approach to Special Hyperbinomial Sequences Fall Classes began September 5, 2006; Final Exams began Friday, Dec 15 Spring 2007 Semester began Tuesday Jan 16; Spring Finals were May 3-9, 2007
20 Jan*: John Duncan Yale Vertex operators and sporadic groups 27 Jan(C) Jason Starr MIT Solutions of families of polynomial equations Colloquium at 4:00 3 Feb no seminar (job interview talks) 10 Feb: Balazs Szegedy IAS Congruence subgroup growth of arithmetic groups in positive characteristic 17 Feb*: Haisheng Li RU-Camden A smash product construction of nonlocal vertex algebras 24 Feb*: Andy Linshaw Brandeis Chiral equivariant cohomology 3 Mar: Wolmer Vasconcelos Rutgers "Complexity of the Normalization of Algebras" 10 Mar: Volodia Retakh Rutgers "Algebras associated to directed graphs and related to factorizations of noncommutative polynomials" 17 Mar: no seminar -------------- Spring Break ------------- 24 Mar no seminar ---- D'Atri Lectures 31 Mar: Chuck Weibel Rutgers "Projective R[t]-modules and cdh cohomology" 7 Apr no seminars in April 5 May Student Body Left Rutgers ---- Final Exam Grading Marathon ------- Classes begin January 18, 2006; Regular classes end Monday May 1. Final Exams are May 4-10, 2006.
9 Sept Colonel Henry Rutgers -------- Department Reception ---------------- 16 Sept: Thuy Pham Rutgers "jdeg of finitely generated graded algebras and modules" note room change to Hill 425 due to Kruskal Conference 23 Sept: Charles Weibel Rutgers "Effective Hodge structures" 30 Sept* Corina Calinescu Rutgers "On certain principal subspaces of standard modules and vertex operator algebras" 7 Oct: Art DuPre Rutgers-Newark "Extensions of Rings and their Endomorphisms" 14 Oct* Katrina Barron Notre Dame "An isomorphism between two constructions of permutation-twisted modules for lattice vertex operator algebras" 21 Oct* Lin Zhang RU+Sequent-Capital "Kazhdan-Lusztig's tensor category and the compatibility condition" 28 Oct: Bob Guralnick USC & IAS "Rational Maps on the Generic Riemann Surface" 4 Nov: Gene Abrams U.Colorado/Colo.Springs "Leavitt path algebras" 11 Nov* Siddhartha Sahi Rutgers "Supercategories and connections" 18 Nov: no seminar 25 Nov: Tom Turkey Plymouth Colony ---------Thanksgiving Break------------ 2 Dec: Earl Taft Rutgers "A class of left quantum groups: Variation on the theme of SL_q(n)" 9 Dec: Harry Tamvakis Brandeis "Quantum cohomology of isotropic Grassmannians" (talk is at 12:30 in H423) 16 Dec*: Hisham Sati U. Adelaide "Mathematical aspects of the partition functions in string theory" Semester begins Thursday September 1, 2005. Regular classes end Tuesday, December 13. Final Exams are Dec.16-23. Math Group Exam time is Friday Dec.16 (4-7PM)
21 Jan: (first Friday of semester) 28 Jan: no seminar Job Interview Talks> 4 Feb: Tom Graber UC Berkeley "Generalizations of Tsen's Theorem" (talk at 4:30 PM) 11 Feb: Pedro Barquero-Salavert CUNY Grad Center "Applications of the transfer method to quadratic forms and sheaves" 18 Feb: Christian Haesemeyer IAS "K-theory and cyclic homology of singularities" 25 Feb: Li Guo RU-Newark "Birkhoff decomposition in QFT and CBH formula" 4 Mar: Earl Taft Rutgers "Exotic Products of Linear Maps on Bialgebras" 11 Mar: Carlo Mazza IAS "Schur Functors and Nilpotence Theorems" 18 Mar: no seminar -------------- Spring Break ------------- 25 Mar: Zhaohu Nie IAS/Stony Brook "Karoubi's construction of Motivic Cohomology Operations" 1 Apr: Gerhard Michler U.Essen/Cornell "Uniqueness proof for Thompson's sporadic simple group" 8 Apr: Bin Shu U.Virginia/E.Normal U. "Representations and Forms of Classical Lie algebras over finite fields" 15 Apr: K. Ebrahimi-Fard Univ.Bonn "Infinitesimal bialgebras and associative classical Yang-Baxter equations" 21 Apr: Bruno Vallette U.Nice "Koszul duality" (Thursday at 1:10 p.m.) 22 Apr: Kate Hurley 29 Apr: Cristiano Husu U.Conn(Stamford) "Relative twisted vertex operators associated with the roots of the Lie algebras A_{1} and A_{2}" 6 May: Student Body Left Rutgers ---- Final Exam Grading Marathon ------- 7 June: Miguel Ferrero UF Rio Grande do Sol, Brazil "PARTIAL ACTIONS OF GROUPS ON ALGEBRAS" (talk at 4 PM) Classes begin January 18, 2005 Spring Break is March 12-20, 2005 Regular classes end Monday May 2. Final Exams are May 5-11, 2005.
10 Sept Colonel Henry Rutgers -------- Department Reception ---------------- 24 Sept* Yom Kippur is 9/25 1 Oct* Liang Kong Rutgers "Conformal field algebras and tensor categories" 8 Oct: MacPherson's 60th Conference 15 Oct: Pavel Etingof MIT "Cherednik and Hecke algebras of orbifolds" 22 Oct* Lin Zhang RU+Sequent-Capital "When does the commutator formula imply the Jacobi identity in Vertex Operator Algebra theory?" 29 Oct*: A. Ocneanu Penn State "Modular theory, quantum subgroups and quantum field theory" 5 Nov: Helmut Hofer Courant D'Atri Lecture: Holomorphic Curve Methods (talk at 1:10 PM) 5 Nov:* Keith Hubbard Notre Dame "Vertex Algebra coalgebras: Their operadic motivation and concrete constructions" 12 Nov: Chuck Weibel Rutgers "Homotopy theory for Motives" 19 Nov: Edwin Beggs Univ. of Wales Swanswa "The Van Est spectral sequences for Hopf algebras" 26 Nov: Tom Turkey Plymouth Colony ----------Thanksgiving Break------------ 10 Dec: Edwin Beggs Univ. of Wales Swanswa"Quasi-Hopf algebras, twisting and the KZ equation" 17 Dec: Student Body Left Rutgers ---- Final Exam Grading Marathon ------- Semester begins Wednesday September 1, 2003. Regular classes end Monday, December 13. Final Exams are Dec.16-23. Math Group Exam time is Thursday Dec.16 (4-7PM)
26 Jan: Diane Maclagan Stanford "Toric Hilbert schemes" (talk at 4:30 PM) 28 Jan: Greg Smith Columbia "Orbifold Cohomology of Toric Stacks" (talk at 11:30 AM) 30 Jan: Anna Lachowska MIT "TBA" (talk at 1:10 PM) 6 Feb: Chuck Weibel Rutgers "A survey of non-Desarguesian planes" 13 Feb: Kia Dalili Rutgers "The HomAB Problem" 20 Feb: Vladimir Retakh Rutgers "An Introduction to A-infinity Algebras" 27 Feb: Vladimir Retakh Rutgers "An Introduction to A-infinity Algebras II" 5 Mar: Remi Kuku IAS "A complete formulation of the Baum-Connes Conjecture for the action of discrete quantum groups" 12 Mar: Amnon Yekutieli Ben Gurion Univ. "On Deformation Quantization in Algebraic Geometry" 19 Mar: no seminar ------------- Spring Break ------------- 26 Mar: Alexander Retakh MIT "Conformal algebras and their representations" 2 Apr: Aaron Lauve Rutgers "Capture the flag: towards a universal noncommutative flag variety" 9 Apr* Stefano Capparelli Univ. Rome "The affine algebra A22 and combinatorial identities" 16 Apr: Uwe Nagel U.Kentucky "Extremal simplicial polytopes" 16 Apr(C) Dale Cutkosky U. Missouri Colloquium Talk at 4:30 PM 23 Apr* Paul Rabinowitz Wisconsin *** D'Atri Lecture at 1:10 PM *** 23 Apr: Li Guo Rutgers-Newark "Dendriform algebras and linear operators" 30 Apr: Earl Taft Rutgers "There exists a one-sided quantum group" 7 May Student Body Left Rutgers ---- Final Exam Grading Marathon -------- Classes begin January 20, 2004; Spring Break is March 13-21, 2004 Regular classes end Monday May 3. Final Exams are May 6-12, 2004. Math Group Final Exam time is Thursday May 6 (4-7PM)
5 Sept George Willis U. South Wales "scale functions on totally disconnected groups" 5 Sept Colonel Henry Rutgers -------- Department Reception ---------------- 8 Sept Various people -------- Gelfand 90th Birthday Celebration -------------- 12 Sept Edwin Beggs U.Wales-Swansea, UK "Constructing tensor categories from from finite groups" 19 Sept Charlie Sims Rutgers "Algorithmic Questions in Rings of Rational Matrices?" 26 Sept David Radnell Michigan Thesis Defense: "Schiffer Variation in Teichmüller space, determinant line bundles and modular functors" 3 Oct* Liang Kong Rutgers "Open-string vertex algebras" 10 Oct C. Musili U.Hyderabad, India "The Development of Standard Monomial Theory" 17 Oct Roy Joshua Inst. Adv. Study "The Motivic DGA" 24 Oct Bodo Pareigis Univ. Munich "Modules, Comodules, Entwinings and Braidings" 31 Oct* Benjamin Doyon Rutgers "From vertex operator algebras to the Bernoulli numbers" 7 Nov* Geoffrey Buhl Rutgers "Complete reducibility and C_n-cofiniteness of vertex operator algebras" 14 Nov no RU seminar ------ Borel Memorial at IAS ----------- 21 Nov* Lin Zhang Rutgers "A vertex operator algebra approach to the construction of a tensor category of Kazhdan-Lusztig" 28 Nov: Tom Turkey ----------Thanksgiving Break------------ 5 Dec* Victor Ostrik IAS "Finite extensions of vertex algebras" 12 Dec* Matt Szczesny U. Penn. "Orbifolding the chiral de Rham complex" Semester begins Tuesday September 2, 2003. Lewis Lectures are the week of October 3rd. Regular classes end Wednesday, December 10. Final Exams are Dec. 15-22. Math Group Exam time is Monday Dec.15 (4-7PM)
28 Jan* Masahiko Miyamoto Japan "Interlocked modules and pseudo-trace functions" 31 Jan: no seminar ------------- Jean Taylor Symposium ------------- 5 Feb: Angela Gibney Michigan "Some open questions about the geometry of the moduli space of curves" 21 Feb* Kiyokazu Nagatomo Japan "Conformal field theory over the projective line" 28 Feb: Jooyoun Hong Rutgers "Normality of Rees algebras for conormal modules" 7 Mar*: Yucai Su Shanghai/Harvard "Lie algebras associated with derivation-simple algebras" 14 Mar* Chengming Bai Nankai&Rutgers "Novikov algebras and vertex (operator) algebras" 21 Mar: no seminar ------------- Spring Break ------------- 28 Mar*: David Radnell Rutgers "Schiffer Variation in Teichmüller Space and Determinant Line Bundles" 3 Apr: Claudio Pedrini U.Genova "Finite dimensional motives" Thursday 3PM - Note change in day! 4 Apr# Hy Bass & Deborah Ball Michigan "Preparing teachers for the mathematical work of teaching" 11 Apr*: Lin Zhang Rutgers "Tensor category theory for modules for a vertex operator algebra -- introduction and generalization" 18 Apr: Constantin Teleman Cambridge U. "Twisted K theory from the Dirac spectral flow" 25 Apr* Michael Roitman Michigan "Affinization of commutative algebras" 2 May: Frederick Gardiner CUNY "The pure mapping class group of a Cantor set" At 1:30 PM - Note change in time! 9 May: Carlo Mazza Rutgers "Schur's Finiteness conditions in tensor categories" At 3:30 PM in H425 - Note change in time and room! Regular classes end Monday May 5. Final Exams are May 8-14, 2003. Math Group Final Exam time is Thursday May 8 (4-7PM)
13 Sep: no seminar Department Reception 20 Sep* YZ Huang Rutgers "Differential equations, duality and modular invariance" 27 Sep* Matthias Gaberdiel Kings College "Conformal field theory and vertex operator algebras" 4 Oct: no seminar 11 Oct: Ravi Rao TATA "Raga Bhimpalasi: The Vaserstein-Suslin Jugalbandhi" 11 Oct(C) Igor Kriz Michigan Colloquium Talk "Conformal field theory and elliptic cohomology" at 4:30 PM 18 Oct: Richard Stanley MIT Jacqueline Lewis Lecture at 4:30PM 18 Oct*: Earl Taft Rutgers "Is there a one-sided quantum group?" 25 Oct:Christian Kassel CNRS-Univ. Louis Pasteur, Strasbourg "Explicit norm one elements for ring actions of finite abelian groups" 25 Oct(C) C. Kassel ""(Strasbourg) Colloquium Talk "Recent developments on Artin's braid groups" at 4:30PM 1 Nov* Benjamin Doyon RU Physics "Twisted vertex operator algebra modules and Bernoulli polynomials" 8 Nov: Charles Weibel RU "The work of Vladimir Voevodsky" 15 Nov* Takashi Kimura IAS/Boston U. "Integrable systems and topology" 22 Nov: Julia Pevtsova IAS "Support Varieties for Finite Group Schemes" 29 Nov: Tom Turkey ----------Thanksgiving Break------------ 6 Dec: Anya Lachowska MIT "Modular group action in the center of the small quantum group"
25 Jan: no seminar Job Interview Talks 1 Feb: no seminar Job Interview Talks 8 Feb* Liz Jurisich College of Charleston "The monster Lie algebra, Moonshine and generalized Kac-Moody algebras" 15 Feb:j Will Toler RU Physics "Low dimensional topology and gauge theory" 22 Feb# Laura Alcock RU Math/Ed "The first course in real analysis in England: figuring out the conceptions students form" 1 Mar: ----- -- CANCELLED 8 Mar*j Benjamin Doyon RU Physics "Vertex Operator Algebras and the Zeta function" 15 Mar*j Gordon Ritter Harvard "Montonen-Olive Duality in Yang-Mills Theory" 22 Mar: no seminar ------------- Spring Break ------------- 29 Mar* Sergei Lukyanov RU Physics "Once again about Bethe Ansatz" 5 Apr:j Benjamin Doyon RU Physics "Fractional Derivatives" 12 Apr: Lisa Carbone RU "Lattice subgroups of Kac-Moody groups over finite fields" 19 Apr: Agata Smoktunowicz Yale/Warsaw(PAS) "A simple nil ring exists" 26 Apr: Earl Taft RU "Recursive Sequences and Combinatorial Identities" 3 May* Yi-Zhi Huang RU "Differential equations and intertwining operators" 10 May: Calculus Profs Rutgers "Grading of Final Exams" Regular classes end Monday, May 6. Final Exams end Wednesday, May 15. Math Group Exam time is Thursday May 9th (4-7PM).
7 Sep: Rutgers Math Department Reception (4PM) 14 Sep* Sasha Kirillov SUNY Stony Brook "On a q-analog of the McKay correspondence" 21 Sep: Ngo Viet Trung Inst.Math.Hanoi "Hilbert functions of non-standard bigraded algebras" 5 Oct: Ed Letzter Temple "Effective Representation Theory of Finitely Presented Algebras" 12 Oct* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories" 19 Oct: V. Retakh Rutgers "Algebra and combinatorics of pseudo-roots of noncommutative polynomials and noncommutative differential polynomials" 26 Oct*: Yan Soibelman Kansas State U. "Elliptic curves and quantum tori" 2 Nov* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories II" 9 Nov* Deepak Parashar MPI Leipzig "Some biparametric examples of Quantum Groups" 16 Nov* Yi-Zhi Huang Rutgers "Vertex operator algebras and conformal field theories III" 23 Nov: Tom Turkey ----------Thanksgiving Break------------ 30 Nov* Hai-Sheng Li Rutgers Camden "Certain noncommutative analogues of vertex algebras" 7 Dec: Chuck Weibel Rutgers "Congruence subgroups of SL2(Z[1/n]), after Serre" 14 Dec: regular classes end Wednesday, December 12. Final Exams are Dec. 15-22. Math Group Exam time is Monday Dec.17 (4-7PM)
26 Jan: Alexei Borodin U.Penn ------- Job Candidate Interview ------- 2 Feb: Chuck Weibel Rutgers "POSTPONED TO March 30" 9 Feb: Dave Bayer Columbia U. "Toric Syzygies and Graph Colorings" 16 Feb: Igor Kriz U.Michigan "A geometric approach to elliptic cohomology" 23 Feb* Yi-Zhi Huang Rutgers "Conformal-field-theoretic analogues of codes and lattices" 2 Mar: Carl Futia Southgate Capital Advisors "Bialgebras of Recursive Sequences and Combinatorial Identities" 9 Mar* Haisheng Li Rutgers Camden "Regular representations for vertex operator algebras" 16 Mar: no seminar ------------- Spring Break ------------- 23 Mar* Yvan Saint-Aubin U.Montreal+IAS "Boundary behavior of the critical 2d Ising model" 30 Mar: Chuck Weibel Rutgers "Functors with transfer (on rings)" 6 Apr*: Richard Ng Towson U "The twisted quantum doubles of finite groups" 13 Apr* Charles Doran Columbia "Variation of the mirror map and algebra-geometric isomonodromic deformations" 20 Apr*: Lev Borisov Columbia "Elliptic genera of singular algebraic varieties" 27 Apr: Diane Maclagan IAS "Supernormal vector configurations, Groebner fans, and the toric Hilbert scheme" 4 May: Calculus Profs Rutgers "Grading of Final Exams" Regular classes end Monday, April 30. Final Exams end Wednesday, May 9. Math Group Exam time is Thursday May 3rd (4-7PM)
8 Sep: Amelia Taylor Rutgers "The inverse Gröbner basis problem in codimension two" 15 Sep* Mike Douglas RU Physics "D-branes" 22 Sep: Chuck Weibel Rutgers "Topological vs. algebraic $K$-theory for complex varieties" 29 Sep: no seminar ------------- Rosh Hoshanna ------------ 6 Oct: Daya-Nand Verma TATA Inst. "Progress Report on the Jacobian Conjecture" 13 Oct: no seminar 20 Oct* Constantin Teleman U.Texas "The Verlinde algebra and twisted K-theory" 27 Oct: Chuck Weibel Rutgers "Homotopy Ends and Thomason Model Categories" 3 Nov* Mirko Primc U.Zagreb "Annihilating fields of standard modules of sl_2~ and combinatorial identities" 10 Nov: Suemi Rodriguez-Romo UNAM Mexico "Quantum Group Actions on Clifford Algebras" 17 Nov: Craig Huneke U.of Kansas "Growth of Symbolic Powers in Regular Local Rings" 24 Nov: Tom Turkey ----------Thanksgiving Break------------ 1 Dec# Nina Fefferman and Matt Young Rutgers VIGRE presentations on p-adic numbers 8 Dec* Mike Douglas? RU Physics "D-branes, instantons and orbifolds"
4 Feb: Martin Sombra IAS+LaPlata "Division formulas and the arithmetic Nullstellensatz" 11 Feb: no seminar 18 Feb: Claudio Pedrini IAS+Genoa "K-theory of algebraic varieties: a Survey" 25 Feb: M.R.Kantorovitz IAS "Andre-Quillen homology from a calculus viewpoint" (with Hochschild homology and algebraic K-theory for dessert) 3 Mar: S. Hildebrandt Bonn *** D'Atri Lecture *** (2-dim. Variational Problems) 10 Mar: D. Christensen IAS "Brown representability in derived categories" 17 Mar: --- ---- ------- Spring Break ----------- 24 Mar* Haisheng Li RU-Camden "Certain extended vertex operator algebras" 31 Mar* Christoph Schweigert Paris "Conformal boundary conditions and three-dimensional topological field theory" 7 Apr: no seminar 14 Apr* Christian Schubert LAPTH France "Multiple Zeta Value Identities from Feynman Diagrams" 21 Apr: no seminar 28 Apr* Tony Milas Rutgers "Structure of fusion rings associated to Virasoro vertex operator algebras" 3 May* (Wednesday) Tony Milas Rutgers "Differential operators and correlation functions"
24 Sep: V. Retakh Rutgers "Noncommutative rational functions+Farber's invariants of boundary links" 1 Oct: Antun Milas* Rutgers "Intertwining operator superalgebras for N=1 minimal models" 8 Oct: Fedor Bogomolov NY Univ "Fundamental Groups of Projective Varieties" 15 Oct: Earl Taft Rutgers "Sequences satisfying a polynomial recurrence" 22 Oct: Yuji Shimizu* Kyoto U "Momentum mappings and conformal fields" 29 Oct: Leon Seitelman U.Conn. SPECIAL VIGRE LECTURE "What's a mathematician like you doing in a place like that" 5 Nov: Keith Pardue IDA/Princeton "Generic Polynomials" 12 Nov: *Haisheng Li Rutgers (Camden) "The Diamond lemma for algebras (following Bergman)" 19 Nov: Yuri Tschinkel U.Illinois "Equivariant compactifications of G_a^n" 26 Nov: Tom Turkey ------Thanksgiving Break-------- 3 Dec: Borisov* Columbia "Vertex algebras and mirror symmetry" 10 Dec: Chongying Dong UC Santa Cruz "Holomorphic orbifold theory, quantum doubles and dual pairs"
22 Jan: P. Balmer Rutgers "The derived Witt group of a ring" 29 Jan: W. Vasconcelos Rutgers "The intertwining algebra" 5 Feb: Thomas Geisser U.Tokyo "TBA" 12 Feb:Dennis Gaitsgory Harvard/IAS "On a VOA of differential operators on a loop group" 19 Feb: Mark Walker Nebraska "The total Chern class map" 26 Feb: Michael Roitman Yale "Universal constructions in conformal and vertex algebras" 5 March: E. Friedlander Northwestern "Re-interpreting the Bloch-Lictenbaum spectral sequence" 12 March: R. Schoen D'Atri Lecture instead of seminar 19 March: Vernal Equinox ------Spring Break March 14-21---- 26 March: Yuji Shimizu Kyoto and Rutgers "Conformal blocks and KZB equations" 2 April: Roger Rabbit Toontown no seminar (Passover/Easter) 9 April: 16 April: Marco Schlichting RU and U. Paris "The negative K-theory of an exact category" 23 April: Chuck Weibel Rutgers "Projective modules over normal surfaces" 30 April: Percy Deift Courant Institute (Colloquium talk) 7 May: Yuji Shimizu Kyoto and Rutgers "Geometric structures underlying some conformal field theories"
18 Sep: Lowell Abrams Rutgers "Modules, comudules and cotensor products over Frobenius algebras" 25 Sep: Bogdan Ion Princeton "Maschke's theorem revisited" 2 Oct: Haisheng Li(*) Rutgers Camden "An infinite-dimensional analogue of Burnside's theorem" 9 Oct: Aron Simis Univ.F.Pernambuco (Recife, Brazil) "Geometric Aspects of Rees Algebras" 16 Oct: A. Beilinson Univ. Chicago Colloquium in honor of Gelfand 23 Oct: Michael Finkelberg(*) IAS/Independent Moscow Univ. "An integrable system on the space of based maps from P^1 to a flag variety" 30 Oct: Yi-Zhi Huang(*) Rutgers "Semi-infinite forms and topological vertex operator algebras" 6 Nov: Alfons Ooms Limburgs Univ, Belgium "On the Gelfand-Kirillov conjecture" 13 Nov: A. Kirillov, Jr.(*) IAS "On the Lego-Teichmuller game" 20 Nov: M.F. Yousif Ohio State-Lima "On three conjectures on quasi-Frobenius Rings" 27 Nov: Tom Turkey ------Thanksgiving Break-------- 4 Dec: C. Lenart Max Planck (Bonn) "" 11 Dec: S. Majid Cambridge Univ. "braided groups and the inductive construction of U_q(g)"
30 Jan: C. Weibel Rutgers "local homology vs. cohomology (after Greenlees-May)" 6 Feb: Brian Parshall U. of Virginia "The cohomology and representation theory of reductive groups in non-describing characteristics" 13 Feb: M. Khovanov(*) Yale and IAS "Lifting the Jones polynomial of knots to invariants of surfaces in 4-space" 20 Feb: Ming-Sun Li Rowan Univ. "Spectral matrices associated to an algebra" 27 Feb: Yi-Zhi Huang(*) Rutgers "Analytic aspects of Intertwining Operators" 6 Mar: Boris Khesin(*) IAS+U.Toronto "Geometric complexification of affine algebras and flat connections on surfaces" 13 Mar: no algebra seminar 20 Mar: Vernal Equinox ------Spring Break-------- 27 Mar: N. Inassaridze Razmadze Inst. "Non-abelian homology of groups" 3 Apr: Jim Stasheff UNCarolina "Physically inspired homological algebra" 10 Apr: Movshev(*) ... QUANTUM MATH SEMINAR 17 Apr: S. Sahi Rutgers "A new character formula for compact Lie groups" 24 Apr: Stefan Schmidt Berkeley "Projective Geometry of Modules" 1 May: Toma Albu U.Wisc.-Milwaukee "GLOBAL KRULL DIMENSION AND GLOBAL DUAL KRULL DIMENSION OF RINGS"
19 Sep: Bill Kantor U. Oregon Colloquium: "Black box classical groups" 26 Sep: Lowell Abrams Rutgers "2-dimensional TQFT's and Frobenius Algebras" 3 Oct: --- ------ Rosh Hoshanna ----- 10 Oct: Tor Gunston Rutgers "Degree functions and linear resolutions" 31 Oct: Chuck Weibel Rutgers "introducing Motives" 7 Nov: --- Columbia Univ. Bass Conference 14 Nov: Stefan Catoiu Temple Univ. "IDEALS OF THE ENVELOPING ALGEBRA U(sl_2)" 21 Nov: M. Kontsevich IHES "Deformation, Quantization and Beyond" 28 Nov: Tom Turkey ------Thanksgiving Break-------- 5 Dec: M. Kontsevich IHES "Deformation, Quantization and Beyond" 12 Dec: C. Pedrini U. Genova "K-Theory and Bloch's Conjecture for complex surfaces"
31 Jan: Luisa Doering Rutgers "Generalized Hilbert functions" 7 Feb: postponed 14 Feb: Miguel Ferrero Porto Alegre,Brazil "Closed and prime submodules of centered bimodules and applications to ring extensions" 21 Feb: Richard Ng Rutgers "Freeness of Hopf algebras over subalgebras" 28 Feb: Siddartha Sahi Rutgers "Introduction to Macdonald polynomials" 7 Mar: Barbara Osofsky Rutgers "Projective dimension for commutative von Neumann regular rings and a new lattice invariant" 14 Mar: Chuck Weibel Rutgers "K-theory and zeta functions on number fields" 21 Mar: ------------ Spring Break ------------ 28 Mar: Carl Faith Rutgers "Rings with ACCs on annihilators" 4 Apr: Joe Brennan N.Dakota "The Ends of Ideals" 11 Apr: Jan Soibelman Kansas State "Meromorphic tensor categories and quantum affine algebras" 18 Apr: Chuck Weibel Rutgers "Tor without identity (after Quillen)" 25 Apr: Wolmer Vasconcelos Rutgers "Integral closure" 2 May: Luca Mauri Rutgers "2 torsors"
20 Sep: C. Weibel Rutgers "the 2-torsion in the K-theory of Z" 27 Sep: Tor Gunston Rutgers "Cohomological dimension of graded modules" 4 Oct: B. Ulrich MichState "Divisor class groups and Linkage" 11 Oct: -- IAS Langlands Fest 18 Oct: Bob Guralnick USC "Finite Orbit Modules and Double Cosets for Algebraic Groups" 25 Oct: Richard Weiss Tufts "Moufang polygons" 1 Nov: Georgia Benkart Wisconsin "Lie Algebras Graded by Finite Root Systems" 8 Nov: Richard Ng Rutgers "On the projectivity of module coalgebras" 15 Nov: -- no seminar 22 Nov: Bill Keigher RU-Newark "The ring of Hurwitz series" 29 Nov: Tom Turkey Thanksgiving (no seminar) 6 Dec: Leon Pritchard RU-Newark "Hurwitz series Formal Functions" 13 Dec: Reading Period after classes
26 Jan: A.Corso Rutgers "generic gaussian ideals" 2 Feb: no seminar 9 Feb: E. Taft Rutgers "Quantum Convolution" 16 Feb: Frosty S. Weather "Snow storm--talks rescheduled" 23 Feb: B. Leasher Rutgers "Geometric Aspects of Steinberg Groups for Jordan Pairs" 1 Mar: L. Mauri Rutgers "Low-dimensional Descent theory" 8 Mar: K.Consani IAS "Double complexes and local Euler factors on algebraic degeneration" 15 Mar: ------------ Spring Break ------------ 22 Mar: YZ Huang Rutgers "On algebraic D-modules and vertex algebras" 29 Mar: Doering&Gunston Rutgers "Algebras Arising from Bipartite Planar Graphs" 5 Apr: Consuelo Martinez Yale "Power subgroups of profinite groups" 12 Apr: M. Singer NC State "Galois theory for difference equations" 19 Apr: C. Weibel Rutgers "Popescu Desingularization (after Swan)" 26 Apr: R. Hoobler CCNY "Merkuriev-Suslin Theorem for arbitrary semi-local rings" 14 May: K. Mimachi Kyushu U. "Quantum Knizhink-Zamolodchikov equation and eigenvalue problem of Macdonald equations"
28 Sep: M.Gerstenhaber U. Penn "Symplectic structures on max. parabolic subgps. of SL_n and boundary solutions of the classical Yang-Baxter equation" 29 Sept:W. Vasconcelos Rutgers "Gauss Lemma" 6 Oct: I. Gelfand Rutgers "Noncommutative symmetric functions" 13 Oct: Joan Elias Barcelona"On the classification of curve singularities" 20 Oct: B. Osofsky Rutgers "Connections between foundations and Algebra" 27 Oct: O. Stoyanov Rutgers "Quantum Unipotent Groups" 3 Nov: I. Gelfand Rutgers "Noncommutative Grassmannians" 10 Nov: M. Tretkoff Stevens "Rohrlich's formula for hypersurface periods" 17 Nov: C. Weibel Rutgers "Tinker Toys and graded modules" 24 Nov: Tom Turkey Thanksgiving Break 1 Dec: Siu-Hung Ng Rutgers "Lie bialgebra structures on the Witt algebra" 8 Dec: E. Zelmanov Yale "On narrow groups and Lie algebras"
27 Jan Alberto Corso Rutgers "Links of irreducible varieties" 3 Feb Chuck Weibel Rutgers "Operads for the Working Mathematician" 10 Feb Maria Vaz Pinto Rutgers "Hilbert Functions and Sally Modules" 17 Feb Yi-Zhi Huang Rutgers "Vertex Operator Algebras for Lay Algebraists" 24 Feb O. Matthieu "On the modular representations of the symmetric group" 3 Mar Claudio Pedrini Genova "The Chow group of singular complex surfaces" 10 Mar B.Sturmfels-Berkly A normal form algorithm for modules over k[x,y]/(xy) 18 Mar ------------ Spring Break ------------ 24 Mar Francesco Brenti IAS "Twisted incidence algebras and Kazhdan-Lusztig-Stanley functions" 31 Mar Myles Tierney Rutgers "Simplicial sheaves" 7 April Wolmer Vasconcelos "A Lemma of Gauss" 14 April Peter Cottontail "Easter's on its way! (Passover too!)" 21 April Susan Morey "Symbolic Powers, Serre Conditions and CM Rees algebras" 28 April K.P. Shum Hong Kong/Maryland "Regular semigroups and generalizations"
29 Jan: Earl Taft Rutgers "Linearly recursive sequences in several variables" 5 Feb: J. Brennan N.D. State "Integral closure of a morphism" 12 Feb: Chuck Weibel Rutgers "Chern classes and torsion in algebraic K-theory" 19 Feb: Friedrich Knop Rutgers "Invariant valuations and eqeuivariant embeddings" 26 Feb: Charles Walters Rutgers "Projectively normal curves" 4 Mar: M.C. Kang Taiwan "Monomial group actions on rational functino fields" 11 Mar: Art Dupre Rutgers-Newark "Extensions and cohomology of groups" 27 Mar: Wolmer Vasconcelos Rutgers "The top of a system of equations" 3 Apr: Marvin Tretkoff Stevens "Some of Dwork's Cohomology Spaces" 17 Apr: Frederico Bien Princeton "Vanishing theorems for D-modules on spherical varieties" 24 Apr: Carl Faith Rutgers "FPF rings"
13 Sep: W. Vogell Martin-Luther U. "Intersection theory" 25 Sep: Sunsook Noh Rutgers "Divisors of 2nd kind and 2-dimensional regular local rings" 2 Oct: W. Vasconcelos Rutgers "The Sally module of a reduction" 9 Oct: Earl Taft Rutgers "Witt and Virasoro algebras as Lie bialgebras" 16 Oct: Bill Hoyt Rutgers TBA 23 Oct: Barbara Osofsky Rutgers TBA 30 Oct: V. Retakh Rutgers "The algebra of extensions without resolutions" 6 Nov: V. Retakh Rutgers continued 13 Nov: A. Brownstein "Generalized Braid groups and motions of strings in 3-space" 20 Nov: Aron Simis U.Fed.Bahia "On tangent cones"
25 Jan Chuck Weibel Rutgers "Operations and symbols in K-theory" 1 Feb Barr Von Oehsen Rutgers "Elliptic genera and Jacobi polynomials" 8 Feb Bernie Johnston FAU TBA 22 Feb Barbara Osofsky Rutgers "Constructing nonstandard uniserial modules over valuation domains" 1 Mar W. Vasconcelos Rutgers "Explicit Nullsatzen" 8 Mar Matt Miller S. Carolina "Betti numbers of modules of finite length" 15 Mar Sam Vovsi Ryder College TBA 21 Mar R.I. Grigorchuk Moscow Inst. "The Burnside problem" 5 Apr Rafael Villareal Rutgers TBA 12 Apr Willie Cortinas Buenos Aires TBA 19 Apr Joachim Lambek McGill U. TBA 26 Apr Charles Walter Rutgers "Algebraic space curves with the expected monomial" 3 May Bernd Ulrich Michigan State "Projective curves and their hypersurface sections"
15 Sep Hisao Tominaga Okayama U. "Some polynomial identites and commutativity of rings" 22 Sep Chuck Weibel Rutgers "Set-theoretic complete intersection points on curves" 6 Oct Carl Faith Rutgers "Subrings of FPF and self-injective rings" 13 Oct W. Vasconcelos Rutgers "Symmetric algebras and syzygies" 20 Oct David Rohrlich Rutgers "maps to the projective line of minimal degree" 27 Oct Stan Page U.Br.Columbia "Slim rings and modules" 3 Nov Joe Johnson Rutgers "Dimension fans and finite presentation of graded modules" 10 Nov Ron Donagi Utah "The Schottky problem" 17 Nov J. Dorfmesiter Muenster "Siegel domains" 24 Nov Barbara Osofsky Rutgers "Strange self-injective rings" 1 Dec Bill Hoyt Rutgers "Division points on generic elliptic curves" 8 Dec Chuck Weibel Rutgers "KABI"
28 Jan S. Goto Brandeis/Nihon U. "On Buchsbaum rings" 4 Feb Chuck Weibel Rutgers "When are projective modules extended?" 11 Feb Barbara Osofsky Rutgers "Between flatness and projectivity" 18 Feb David Rohrlich Rutgers "An intro to L-functions on elliptic curves" 25 Feb M. Takeuchi IAS "Commutative Hopf algebras and cocommutative Hopf algebras in char. p" 04 Mar Harry Gonshor Rutgers "Conway numbers and semigroup rings" 11 Mar Louis Rowen Yale "Finite dimensional division algebras" 25 Mar Bill Hoyt Rutgers "Periods of abelian integrals" 1 Apr Don Schack U. Buffalo "Deformations of diagrams" 8 Apr Earl Taft Rutgers "Hopf algebras" 15 Apr Chuck Weibel Rutgers "Witt vectors made easy" 22 Apr Jan van Geel U. Antwerp "Primes and value functions" 29 Apr Dick Cohn Rutgers "The General Solution in Differential Equations"
25 Sept Earl Taft Rutgers "A generalization of divided power sequences" 1 Oct Moss Sweedler Cornell "Products of flat modules" 8 Oct Chuck Weibel Rutgers "Principal ideals and smooth curves" 15 Oct Joe Johnson Rutgers "Rings that lack ..." 22 Oct Wolmer Vasconcelos Rutgers TBA 29 Oct Richard Block UC Riverside "Irreducuble representations of skew polynomial rings" 5 Nov M. Gerstenhaber U.Penn "On the deformation of differential graded algebras" 7 Nov F. Orecchia U.Genoa "Tangent cones and singularities of algebraic curves" 12 Nov E. Sontag Rutgers "PL Algebras" 19 Nov Dick Bumby Rutgers "Jacobi symbols" 3 Dec Carl Faith Rutgers "Noncommutative rings"
Derived categories of moduli spaces of stable rational curves
(Ana-Maria Castravet, March 28, 2018):
x
In the second part of my talk I will focus on noncommutative symplectic
forms and noncommutative Poisson geometry. This is where the
double Gerstenhaber algebra of noncommutative poly-vector fields
appears. I will show that use of skew-symmetric properties allows us
to substantially simply the definition.
Since this is a seminar aimed at the general audience, I'll start by
explaining the notion of vertex algebra, as well as the physical meaning.
Then I'll introduce the notion of a MOSVA and the physical meaning.
Hopefully there will be some time to explain what I have done.
I will start by reviewing an $H_0$-Poisson structure --- a
noncommutative analog of the Poisson bracket and related notion of
double Poisson brackets. We will see how an $H_0$-Poisson structure
descends to a usual Poisson bracket on the moduli space of
representations of the underlying associative algebra. I will then
show how one can substantially modify definition of double Poisson
bracket by M. Van den Bergh to provide a number of new nontrivial
examples.
The talk is aimed at graduate students. In particular, while
some familiarity with Chern classes would be useful, I will introduce the
necessary notions during the talk.
The talk will survey some aspects of this ongoing search.
The methods for studying this question involve explicit and constructive
applications of well known classical theorems in algebra and group theory,
for instance Conway's and Pless' application of Burnside's orbit counting
theorem and quadratic reciprocity dating back to the 1980's.
More recent and partly computational methods are based on
representation theory of finite groups.
Computations in intersection theory
(Dan Grayson, Oct. 17, 2012):
On the slice filtration for hermitian K-theory
(Oliver Rondigs, November 7, 2012):
Injectivity property of etale H^1, non-stable K_1, and other functors
(Anastasia Stavrova, December 5, 2012):
Exhausting quantization procedures
(Vasily Dolgashev, Jan. 25, 2012):
Shift Equivalence and Z[t]-modules (Chuck Weibel, February 8, 2012):
K-theory of minuscule varieties (Anders Buch, February 22, 2012):
From algebra to category theory: a first approach to fusion categories
The idea of this talk is to introduce and motivate the
notion of fusion category. We shall give some basic definitions
and examples that help us understand this structure.
We shall introduce the ideas of gradings, solvability and
nilpotency for fusion categories and we shall connect it to the
corresponding ideas for groups. We shall also discuss some
results concerning to the structure of fusion categories with
restrictions on the Frobenius-Perron dimensions of its simple
objects.
Invariants of Matrix Factorizations
(Mark Walker, March 21, 2012):
Combinatorial aspects of toric mirror symmetry
(Lev Borisov, March 28, 2012):
Noncommutative Laurent Phenomena
(Vladimir Retakh, April 11, 21012:
Symmetric subgroup orbit closures on flag varieties
as universal degeneracy loci
We will describe a method for computing formulas for the S-equivariant
fundamental classes of such orbit closures, where S is a maximal torus
of K. The main idea is to use equivariant localization and the
self-intersection formula to "guess" formulas for the classes of closed
orbits, and then to compute formulas for the remaining orbit closures
using divided difference operators. In type A, we will also describe
how these formulas can be interpreted as Chern class formulas for
classes of certain types of degeneracy loci involving a vector bundle
over a scheme which is equipped with a complete flag of subbundles and
an additional structure determined by K. This is analogous to (and
motivated by) work of W. Fulton on Schubert varieties in flag bundles,
their role as universal degeneracy loci for maps of flagged vector
bundles, and connections between that work and the torus-equivariant
cohomology of the flag variety described by W. Graham.
The Schottky Problem and genus 5 curves
(Charles Siegel, Sept. 14, 2011):
Congruence subgrous of lattices in rank 2 Kac-Moody groups
over finite fields
Cluster algebras and combinatorics of rigid objects
in 2 Calabi-Yau categories
I shall recall the definition of cluster algebras and how to construct
the cluster categories associated with them (the latter are
2-Calabi-Yau categories). Then I will introduce the combinatorial
invariant that will help prove part of the conjectures on g-vectors
associated to cluster variables.
Giambelli formulas for orthogonal Grassmannians
(Anders Buch, October 26, 2011):
On Fourier-Mukai type functors
(Alice Rizzardo, November 2, 2011):
Comparison of Dualizing Complexes
(Changlong Zhong, November 9, 2011):
Homotopical Methods in Algebraic Geometry
(Pablo Pelaez, November 30, 2011):
Syzygies of binomial ideals and toric Eisenbud-Goto conjecture
(Lev Borisov, April 6, 2011):
Cyclic homology, simplicial rapid decay algebras, and applications to K*t(l¹(G))
Rational points, zero cycles of degree one, and A^1-homotopy theory
(Christian Haesemeyer, Feb. 16, 2011):
Quantum differential operators (Uma Iyer, Sept. 20, 2010):
Monoids and algebraic geometry (Chuck Weibel, Sept. 27, 2010):
Dimensions of fixed point spaces of elements in linear groups
(Bob Guralnick, Oct. 4, 2010)
Etale cohomology operations (Chuck Weibel, Oct. 25, 2010)
Pieri rules for the K-theory of cominuscule Grassmannians
(Anders Buch, Nov. 8, 2010) I will present positive
combinatorial formulas for the structure constants in products
involving special Schubert classes on any cominuscule Grassmannian.
Together with a result of Clifford, Thomas, and Yong, this proves a
K-theoretic Littlewood-Richardson rule for maximal orthogonal
Grassmannians. This is joint work with Vijay Ravikumar.
The Lie product in the continuous Lie dual of the Witt Algebra
(Earl Taft, Nov. 29, 2010):
Motivic cohomology operations (Chuck Weibel, Dec. 6, 2010)
Algebraic Structures from Operads
(Ralph Kaufmann, Dec. 13, 2010):
Periodicity of hermitian K-groups
(Max Karoubi, Feb. 1, 2010):
Applications of stable bundles to Witt groups and Brauer groups
(Ray Hoobler, Mar. 1, 2010):
Drinfeld twists and finite groups
(Christian Kassel, Mar. 8, 2010):
Hopf algebras and recursive sequences
(Earl Taft, Mar. 22, 2010):
Tilting 1 (Chuck Weibel, March 29, 2010):
Tilting 2 (Chuck Weibel, April 19, 2010):
Tilting 3 (Robert Wilson, April 26, 2010):
Module Structures on the Ring of Hurwitz Series
Bill Keigher, May 3, 2010):
Differential Central Simple Algebras and Picard-Vessiot representations
(Lourdes Juan, Oct. 5, 2009):
Derangements in Finite and Algebraic Groups
(Bob Guralnick, Oct. 12, 2009):
Mathematics arising from a new look at the
Dedekind-Frobenius group matrix and group determinant
(Ken Johnson, Oct. 19, 2009):
Induced definable structure on cyclic subgroups of the free group
The classfication problem for finite rank dimension groups
(Paul Ellis, Nov. 9, 2009):
Picard-Vessiot Theory (Ravi Srinivasan, Nov.16, 2009):
Stability conditions for triangulated categories
(Chuck Weibel, Feb. 2, 2009):
Partitioned Differential Quasifields
(Leon Pritchard, Feb. 23, 2009):
Stability conditions in Physics (Jan Manschot, March 2, 2009):
The Nekrasov Conjecture for Toric Surfaces
(Elizabeth Gasparim, March 30, 2009):
Differential Quasifields (Bill Keigher, April 13, 2009):
Morphisms of cohomological field theories and
behavior of Gromov-Witten invariants under quotients
higher order Hochschild (co)homology
(Gregory Ginot, April 27, 2009):
Morita Equivalence Revisited (Paul Baum, Sept. 5, 2008):
This talk studies an equivalence relation
between k-algebras which is a weakening of Morita
equivalence. If A and B are equivalent in the new equivalence
relation, then A and B have isomorphic periodic cyclic
homology, and Prim(A) is in bijection with Prim(B). However, the
bijection between Prim(A) and Prim(B) might not be
a homeomorphism. Thus the new equivalence relation permits a tearing
apart of strata in the primitive ideal spaces
which is not allowed by Morita equvalence. An application to the
representation theory of p-adic groups will be briefly
indicated. This talk is intended for non-specialists. All the basic
definitions will be carefully stated.
Formality theorems for Hochschild (co)chains and their applications
(Vasily Dolgushev, Sept. 18, 2008):
Rationality and integrality in dynamical systems
(Mike Zieve, Sept. 22, 2008):
Combinatorial identities and Hopf algebras
(Earl Taft, October 20, 2008):
Infinite towers of cocompact lattices in Kac-Moody groups
(Leigh Cobbs, November 3, 2008):
K-theory of some algebras associated to quivers
(Guillermo Cortiñas, November 14, 2008):
Reduced K-theory of Azumaya algebras
(Roozbeh Hazrat, December 1, 2008):
The theory of Azumaya algebras developed parallel to the theory of
central simple algebras. However the latter are algebras over fields
whereas the former are algebras over rings. One wonders how the K-theory
of these objects compare to each other. We look at higher K-theory and
reduced K-theory of these objects. We ask nice questions!
W-algebras, quantum groups and combinatorial identities
(Antun Milas, Feb. 5, 2008):
The lattice of subfields of K(x)
(Mike Zieve, Feb. 8, 2008:
Complex dynamics and shift automorphism groups
(Zin Arai, Feb. 11, 2008):
In this talk, we consider the monodromy homomorphism for the complex
Henon map, a 2-dimensional analog of the quadratic map. We need the
shift space of bi-infinite sequences in this case, and the automorphism
group of this space is much more complicated than that of the one-sided
shift space. We propose a computer-assisted method to compute the
monodromy homomorphism and show that automorphisms of the shift space
can be used to determine the dynamics of the real Henon map.
Automorphism groups of curves
(Mike Zieve, Feb. 25, 2008):
Model categories versus derived categories
(Chuck Weibel, March 3, 2008):
Rational points on homogeneous spaces
(Parimala, March 10, 2008):
Formal differential representations, Faa di Bruno and the Riordan Group
Real Groups and Topological Field Theory
David Ben-Zvi, March 28, 2008:
Singularities in geometry, topology and strings,
Antonella Grassi, May 9, 2018):
I will discuss a "Brieskorn-Grothendieck" program involving certain
singularities, Lie algebras and representations. These singularities
arise in many different areas of mathematics and physics. I will
focus on the case of complex 3 dimensional spaces relating to
algebraic geometry, topology and physics. I will disucss local,
global and local-to-global properties of threefolds with certain
singularities and crieteria for these threefolds to be rational
homology manifolds and conditions for threefolds to satisfy rational
Poincar\'e duality.
We state a conjecture on the extension of
Kodaira's classification of singular fibers on relatively minimal
elliptic surfaces to the class of birationally equivalent relatively
minimal genus one fibered varieties and we give results in this
direction.
Hodge theory and o-minimal geometry
(Benjamin Bakker, May 2, 2018):
Hodge structures on cohomology groups are fundamental invariants of algebraic
varieties; they are parametrized by quotients $D/\Gamma$ of periods domains by
arithmetic groups. Except for a few very special cases, such quotients are
never algebraic varieties, and this leads to many difficulties in the general
theory. We explain how to partially remedy this situation by equipping
$D/\Gamma$ with an o-minimal structure, and show that period maps are
"definable" with respect to this structure.
As a consequence, we obtain an
easy proof of a result of Cattani--Deligne--Kaplan on the algebraicity of
Hodge loci, a strong piece of evidence for the Hodge conjecture. The proof of
the main theorem relies heavily on work of Schmid, Kashiwara, and
Cattani--Kaplan--Schmid on the asymptotics of degenerations of Hodge
structures. This is joint work with B. Klingler and J. Tsimerman.
Singularities of general fibers in positive characteristic
(Joe Waldron, April 18, 2018):
Generic smoothness fails to hold for some fibrations in positive
characteristic. We study consequences of this failure, in
particularly by obtaining a canonical bundle formula relating a fiber
with the normalization of its maximal reduced subscheme. This has
geometric consequences, including that generic smoothness holds on
terminal Mori fiber spaces of relative dimension two in characteristic
$p\geq 11$. This is joint work with Zsolt Patakfalvi.
Conformal blocks attached to twisted groups
(Chiara Damiolini, April 11, 2018):
Let $G$ be a simple and simply connected algebraic group over $\mathbb{C}$.
We can attach to $G$ the sheaf of conformal blocks: a vector bundle on
$M_{g}$ whose fibres are identified with global sections of a certain
line bundle on the stack of $G$-torsors. We generalize the
construction of conformal blocks to the case in which $\mathcal{G}$ is
a twisted group over a curve which can be defined in terms of covering
data. In this case the associated conformal blocks define a sheaf on a
Hurwitz space and have properties analogous to the classical case.
A question of Manin is whether the derived category of the
Grothendieck-Knudsen moduli space $M_{0,n}$ of stable, rational curves
with n markings admits a full, strong, exceptional collection that is
invariant under the action of the symmetric group $S_n$. I will present
an approach towards answering this question. In particular, I will
explain a construction of an invariant full exceptional collection on
the Losev-Manin space. This is joint work with Jenia Tevelev.
The indeterminacy of universal Abel-Jacobi sections
(Nicola Pagani, March 14, 2018):
The (universal) Abel-Jacobi maps are the sections of the forgetful
morphism from the universal Jacobian to the corresponding moduli space
$M_{g,n}$ of smooth pointed curves. When the source and target moduli spaces
are compactified, these sections are only rational maps, and it is
natural to ask for the largest locus where each of them is a
well-defined morphism. We explicitly characterize this locus, which
depends on the chosen compactification of the universal Jacobian (for
the source we fix the Deligne-Mumford compactification $\bar{M}_{g,n}$
by means of stable curves). In particular, we deduce that for every
Abel-Jacobi map there exists a compactification of the universal
Jacobian such that the map extends to a well-defined morphism on
$\bar{M}_{g,n}$. We apply this to the problem of defining and computing
several different extensions to $\bar{M}_{g,n}$ of the double
ramification cycle (= the locus of smooth pointed curves that admit a
meromorphic function with prescribed zeroes and poles at the points).
This is a joint work with Jesse Kass.
Algebraic dynamics from topological and holomorphic dynamics
(Rohini Ramadas, Feb. 28, 2018):
Let $f:S^2 \to S^2$ be an orientation-preserving branched covering from
the 2-sphere to itself whose postcritical set
$P := \{ f^n(x) | x\ \mathrm{is\ a\ critical\ point\ of\ f\ and}\ n>0 \}$
is finite.
Thurston studied the dynamics of $f$ using an induced holomorphic
self-map $T(f)$ of the Teichmuller space of complex structures on
$(S^2, P)$. Koch found that this holomorphic dynamical system on
Teichmuller space descends to algebraic dynamical systems:
1. $T(f)$ always descends to a multivalued self map $H(f)$ of the moduli
space $M_{0,P}$ of markings of the Riemann sphere by the finite set $P$
2. When $P$ contains a point $x$ at which $f$ is fully ramified,
under certain combinatorial conditions on $f$, the inverse of $T(f)$
descends to a rational self-map $M(f)$ of projective space $P^n$. When,
in addition, $x$ is a fixed point of $f$, i.e. $f$ is a
`topological polynomial', the induced self-map $M(f)$ is regular.
The dynamics of $H(f)$ and $M(f)$ may be studied via numerical invariants
called dynamical degrees: the k-th dynamical degree of an algebraic
dynamical system measures the asymptotic growth rate, under iteration,
of the degrees of k-dimensional subvarieties.
I will introduce the dynamical systems $T(f)$, $H(f)$ and $M(f)$, and
dynamical degrees. I will then discuss why it is useful to study $H(f)$
(resp. $M(f)$) simultaneously on several compactifications of $M_{0,P}$.
We find that the dynamical degrees of $H(f)$ (resp. $M(f)$) are
algebraic integers whose properties are constrained by the dynamics of $f$
on the finite set $P$. In particular, when $M(f)$ exists, then the more
$f$ resembles a topological polynomial, the more $M(f): P^n \to P^n$
behaves like a regular map.
Curves, maps, and singularities in genus one
(Dhruv Ranganathan, February 21, 2018):
I will outline a new framework based on tropical and logarithmic methods to
study genus one curve singularities and discuss its relationship with the
geometry of moduli spaces. I will focus on two applications of these ideas.
First, they allow one to explicitly factorize the rational maps among
log canonical models of the moduli space of n-pointed elliptic curves.
Second, they reveal a modular interpretation for Vakil and Zinger's famous
desingularization of the space of elliptic curves in projective space, a short
conceptual proof of that result, and several new generalizations.
Time permitting, though it rarely does, I will mention some applications
to both classical and virtual enumerative geometry. This is based on work with
Len and with Santos-Parker and Wise, as well as ongoing work with Battistella
and Nabijou.
Equations of Cartwright-Steger surface
(Lev Borisov, February 7, 2018):
Cartwright-Steger surface is an algebraic surface of general type
which appeared in the study of fake projective planes.
I will describe the technique that allowed us to find equations of it,
in its bicanonical embedding. This is a joint work with Sai Kee Yeung.
An arithmetic site of Connes-Consani type for Gaussian integers
(Aurélien Sagnier, Jan. 24, 2018):
Connes and Consani proposed to study the action of the multiplicative
monoid of positive integers $\mathbb{N}^\times$
on the tropical semiring $(\mathbb{Z},max,+)$,
as an approach to the Riemann zeta function. This construction depends
upon the ordering on the reals. I will first explain their approach,
then give an extension of this construction to the Gaussian integers.
Fall 2017
Gonality of complete intersection curves
(Brooke Ullery, Dec. 13, 2017:
The gonality of a smooth projective curve is the smallest degree of a map
from the curve to the projective line. If a curve is embedded in projective
space, it is natural to ask whether the gonality is related to the embedding.
In my talk, I will discuss recent work with James Hotchkiss. Our main result
is that, under mild degree hypotheses, the gonality of a complete intersection
curve in projective space is computed by projection from a codimension 2
linear space, and any minimal degree branched covering of $\mathbb P^1$
arises in this way.
Equivariant K-theory associated to Kac-Moody groups
(Seth Baldwin, Dec. 6, 2017):
The cohomology ring of flag varieties has long been known to exhibit
positivity properties. One such property is that the structure constants
of the Schubert basis with respect to the cup product are non-negative.
Brion (2002) and Anderson-Griffeth-Miller (2011) have shown that positivity
extends to K-theory and T-equivariant K-theory, respectively. In this talk
I will discuss recent work (joint with Shrawan Kumar) which generalizes
these results to the case of Kac-Moody groups.
Local-global principles for rational points and zero-cycles
(Julia Hartmann, Nov. 15, 2017):
Given a variety over a field $F$ and a collection of overfields of
$F$, one may ask whether the existence of rational points over each of
the overfields (local) implies the existence of a rational point over
$F$ (global). Such local-global pinciples are a main tool for
understanding the existence of rational points on varieties.
In this talk, we study varieties that are defined over semi-global
fields, i.e., function fields of curves over a complete discretely
valued field. A semi-global field admits several natural collections
of overfields which are geometrically motivated, and one may ask for
local-global principles with respect to each such collection. We
exhibit certain cases in which local-global principles for rational
points hold. We also show that local-global principles for zero-cycles
of degree one hold provided that local-global principles hold for the
existence of rational points over extensions of the function
field. This last assertion is analogous to a known result for
varieties over number fields.
(Joint work with J.-L. Colliot-Thélène, D. Harbater, D. Krashen,
R. Parimala, and V. Suresh)
Explicit equations of a fake projective plane
(Lev Borisov, Nov. 8, 2017):
Fake projective planes are complex algebraic surfaces of general type
whose Betti numbers are the same as that of a usual projective plane.
The first example was constructed by Mumford about 40 years ago
by 2-adic uniformization. There are 50 complex conjugate pairs of such
surfaces, given explicitly as ball quotients (Cartwright+Steger).
However, a ball quotient description does not on its own lead to an
explicit projective embedding. In a joint work with JongHae Keum, we
find equations of one pair of fake projective planes in bicanonical
embedding, which is so far the only result of this kind.
Birational geometry of moduli spaces of parabolic bundles
(Han-Bom Moon, October 18, 2017):
I will describe a project on birational geometry of the moduli space
of parabolic bundles on the projective line in the framework of
Mori's program, and its connection with classical invariant theory
and conformal blocks. This is joint work with Sang-Bum Yoo.
Linear Systems on General Curves of Fixed Gonality
(David Jensen, Oct. 4, 2017:
The geometry of an algebraic curve is governed by its linear
systems. While many curves exhibit bizarre and pathological linear
systems, the general curve does not. This is a consequence of the
Brill-Noether theorem, which says that the space of linear systems of
given degree and rank on a general curve has dimension equal to its
expected dimension. In this talk, we will discuss a generalization of
this theorem to general curves of fixed gonality. To prove this
result, we use tropical and combinatorial methods.
This is joint work
with Dhruv Ranganathan, based on prior work of Nathan Pflueger.
Character levels and character bounds
(Pham Huu Tiep, September 27, 2017):
We develop the concept of character level for the complex irreducible
characters of finite, general or special, linear and unitary
groups. We give various characterizations of the level of a character
in terms of its Lusztig's label, of its degree, and of certain dual
pairs. This concept is then used to prove exponential bounds for
character values, provided that either the level of the character or
the centralizer of the element is not too large. This is joint work
with R. M. Guralnick and M. Larsen.
K-classes of Brill-Noether loci and a determinantal formula
(Nicola Tarasca, September 20, 2017):
I will present a formula for the Euler characteristic of the
structure sheaf of Brill-Noether loci of linear series on curves with
prescribed vanishing at two marked points.
The formula recovers the classical Castelnuovo number in the
zero-dimensional case, and previous work of Eisenbud-Harris, Pirola,
Chan-López-Pflueger-Teixidor in the one-dimensional case. The
result follows from a new determinantal formula for the K-theory class
of certain degeneracy loci of maps of flag bundles.
This is joint work with Dave Anderson and Linda Chen.
A general algebraic structure theory for tropical mathematics
(Louis Rowen, September 13, 2017):
We study triples (A,T,-) of a set A with algebraic structure
(such as a semiring), a subset T and a negation operator '-' on T.
A key example is the max-plus algebra T. This viewpoint enables
one to view the tropicalization functor as a morphism,
suggesting tropical analogs of classical structures such as
Grassmann algebras, Lie algebras, Lie superalgebras, Poisson
algebras, and Hopf algebras.
Spring 2017
Equivariant quantum K-theory of projective space
(Sjuvon Chung, April 26, 2017):
Recent developments of Buch-Chaput-Mihalcea-Perrin have allowed for a closer
look at the quantum K-theory of cominuscule flag varieties. For example,
their Chevalley formula allows one to compute quantum K-theoretic products
involving Schubert divisor classes. In the special case of projective space,
one can extend this Chevalley formula to describe products of arbitrary
Schubert classes. We shall discuss this extension along with some of its
potential combinatorial and representation-theoretic consequences.
Schubert calculus
(Anders Buch, April 19, 2017):
The cohomology ring of a flag variety has a natural basis of Schubert
classes. The multiplicative structure constants with respect to this
basis count solutions to enumerative geometric problems; in particular
they are non-negative. For example, the structure constants of a
Grassmannian are the classical Littlewood-Richardson coefficients,
which show up in numerous branches of mathematics.
I will speak about a new puzzle-counting formula for the structure constants
of 3-step partial flag varieties that describes products of classes that are
pulled back from 2-step flag varieties. By using a relation between
quantum cohomology of Grassmannians and classical cohomology of 2-step
flag varieties, this produces a new combinatorial formula for the (3
point, genus zero) Gromov-Witten invariants of Grassmannians, which is
in some sense more economical than earlier formulas.
Kirillov-Reshetikhin modules and Macdonald polynomials:
a survey and applications (Christian Lenart, April 5, 2017):
This talk is largely self-contained.
In a series of papers with S. Naito, D. Sagaki, A. Schilling, and
M. Shimozono, we developed a uniform combinatorial model for (tensor products
of one-column) Kirillov-Reshetikhin (KR) modules of affine Lie algebras. We
also showed that their graded characters coincide with the specialization of
symmetric Macdonald polynomials at $t=0$, and extended this result to
non-symmetric Macdonald polynomials. I will present a survey of this work and
of the recent applications, which include: computations related to KR
crystals, crystal bases of level 0 extremal weight modules, Weyl modules
(local, global, and generalized), $q$-Whittaker functions, and the quantum
$K$-theory of flag varieties.
Dynamics and polynomial invariants for free-by-cyclic groups
(Ilya Kapovich, March 22, 2017):
We develop a counterpart of the Thurston-Fried-McMullen "fibered
face" theory in the setting of free-by-cyclic groups, that is,
mapping tori groups of automorphisms of finite rank free groups. We
obtain information about the BNS invariant of such groups, and
construct a version of McMullen's "Teichmuller polynomial" in the
free-by-cyclic context. The talk is based on joint work with Chris
Leininger and Spencer Dowdall.
Decompositions of Grothendieck polynomials (Oliver Pechenik, March
8, 2017):
Finding a combinatorial rule for the Schubert structure constants
in the K-theory of flag varieties is a long-standing problem.
The Grothendieck polynomials of Lascoux and Schützenberger (1982)
serve as polynomial representatives for K-theoretic Schubert classes,
but no positive rule for their multiplication is known outside of
the Grassmannian case.
We contribute a new basis for polynomials, give a positive
combinatorial formula for the expansion of Grothendieck polynomials
in these "glide polynomials", and provide a positive combinatorial
Littlewood-Richardson rule for expanding a product of Grothendieck
polynomials in the glide basis. A specialization of the glide basis
recovers the fundamental slide polynomials of Assaf and Searles
(2016), which play an analogous role with respect to the Chow ring of
flag varieties. Additionally, the stable limits of another
specialization of glide polynomials are Lam and Pylyavskyy's (2007)
basis of multi-fundamental quasisymmetric functions, K-theoretic
analogues of I. Gessel's (1984) fundamental quasisymmetric
functions. Those glide polynomials that are themselves quasisymmetric
are truncations of multi-fundamental quasisymmetric functions and form
a basis of quasisymmetric polynomials. (Joint work with D. Searles).
The Witt group of surfaces and 3-folds (Chuck Weibel, March 1, 2017):
If V is an algebraic variety, the Witt group is formed from vector bundles
equipped with a nondegenerate symmetric bilinear form. When it has
dimension <4, it embeds into the more classical Witt group of the function
field (Witt 1934). When V is defined over the reals, versions of the
discriminant and Hasse invariant enable us to determine W(V).
Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian
(Ryan Shifler, February 23, 2017):
The odd symplectic Grassmannian IG:=IG(k, 2n+1) parametrizes k
dimensional subspaces of $\mathbb{C}^{2n+1}$ which are isotropic with respect to
a general (necessarily degenerate) symplectic form. The odd symplectic
group acts on IG with two orbits, and IG is itself a smooth Schubert
variety in the submaximal isotropic Grassmannian IG(k, 2n+2). We use
the technique of curve neighborhoods to prove a Chevalley formula in
the equivariant quantum cohomology of IG, i.e. a formula to multiply a
Schubert class by the Schubert divisor class. This generalizes a
formula of Pech in the case k=2, and it gives an algorithm to
calculate any quantum multiplication in the equivariant quantum
cohomology ring. The current work is joint with L. Mihalcea.
Fall 2016
Vector bundles of conformal blocks on the moduli space of curves
(Angela Gibney, December 14, 2016):
In this talk I will introduce the moduli space of curves and a class of
vector bundles on it. I'll discuss how these bundles, which have
connections to algebraic geometry, representation theory, and
mathematical physics, tell us about the moduli space of curves,
and vice versa, focusing on just a few recent results and open problems.
Geometry and the arithmetic of algebraic structures
(Daniel Krashen, December 7, 2016):
Algebraic structures, such as central simple algebras and quadratic forms,
play an important role in understanding the arithmetic of fields. In
this talk, I will explore the use of homogeneous varieties in working
with these structures, examining in particular the splitting fields of
central simple algebras, and the problem of determining the maximal
dimension of anisotropic quadratic forms over a given field.
Double Gerstenhaber algebras of noncommutative poly-vector fields
(Semeon Artamonov, November 30, 2016):
I will first review the algebra of poly-vector fields and differential
forms in noncommutative geometry, and specific features of this
generalization of conventional (commutative) differential geometry.
Representations of p-DG 2-categories (Robert Laugwitz,
November 16, 2016):
2-representations for k-linear 2-categories with certain finiteness
conditions were studied in a series of papers by Mazorchuk-Miemietz
2010-2016. A central idea is the construction of categorifications of
simple representations (so-called simple transitive 2-representations)
as 2-cell representations (inspired by the Kazhdan-Lusztig cell
theory to construct simple representations for Hecke algebras).
This
talk reports on joint work with V. Miemietz (UEA) adapting this
2-representation theory to a p-dg enriched setting. This approach is
motivated by recent results on the categorification of small quantum groups at
roots of unity (by Elias-Qi) which uses techniques from Hopfological
algebra developed by Khovanov-Qi.
Rees-like Algebras and the Eisenbud-Goto Conjecture (Jason
McCullough, November 9, 2016):
Regularity is a measure of the computational complexity of a
homogeneous ideal in a polynomial ring. There are examples in which
the regularity growth is doubly exponential in terms of the degrees of
the generators but better bounds were conjectured for "nice" ideals.
Together with Irena Peeva, I discovered a construction that overturns
some of the conjectured bounds for "nice" ideals - including the
long-standing Eisenbud-Goto conjecture. Our construction involves two
new ideas that we believe will be of independent interest: Rees-like
algebras and step-by-step homogenization. I'll explain the
construction and some of its consequences.
The Intricate Maze of Graph Complexes
(Vasily Dolgushev), November 2, 2016):
I will talk about several families of cochain complexes
"assembled from" graphs. Although these complexes (and their
generalizations) are easy to define, it is very hard to get
information about their cohomology spaces. I will describe links
between these graph complexes, finite type invariants of knots, the
Grothendieck-Teichmueller Lie algebra, deformation quantization and
the topology of embedding spaces. I will conclude my talk with several
very intriguing open questions.
K-theoretic Schubert calculus
(Oliver Pechenik, October 26, 2016):
The many forms of the celebrated Littlewood-Richardson rule give combinatorial
descriptions of the product structure of Grassmannian cohomology. Anders Buch
(2002) was the first to extend one of these forms to the richer world of
K-theory. I will discuss joint work with Alexander Yong on lifting another
form from cohomology to K-theory. This latter form has the advantage of
extending further to give the first proved rule in torus-equivariant K-theory,
as well as partially extending to the case of isotropic Grassmannians.
Quantum Kostka and the rank one problem for $\mathfrak{sl}_{2m}$
(Natalie Hobson, October 19, 2016):
In this talk we will define and explore an infinite family of vector
bundles, known as vector bundles of conformal blocks, on the
moduli space M0,n of marked curves. These bundles arise
from data associated to a simple Lie algebra. We will show
a correspondence (in certain cases) of
the rank of these bundles with coefficients in the cohomology of the
Grassmannian. This correspondence allows us to use a formula for
computing "quantum Kostka" numbers and explicitly characterize
families of bundles of rank one by enumerating Young tableau.
We will show these results and illuminate the methods involved.
Elliptic Curves and Modular Forms
(Ed Karasiewicz, October 12, 2016):
The Modularity Theorem describes a relationship between elliptic curves and
modular forms. We will introduce some of the concepts needed to describe this
relationship. Time permitting we will discuss some applications to certain
diophantine equations.
Euler characteristics in cominuscule quantum K-theory
(Sjuvon Chung, October 5, 2016):
Equivariant quantum K-theory is a common generalisation of algebraic
K-theory, equivariant cohomology and quantum cohomology. We will
present a brief overview of the theory before we discuss recent results on
three peculiar properties of equivariant quantum K-theory for cominuscule flag
varieties. This is joint work with Anders Buch.
Quaternionic Discrete Series (Zhuohui Zhang, September 28, 2016):
I will give a brief introduction to the construction and geometric
background of quaternionic discrete series, and how
to study them based on examples.
Quaternionic discrete series are representations of a real Lie group
$G$ which can be realized on a Dolbeault cohomology group of the
twistor space of the symmetric space of $G$.
What is a meromorphic open string vertex algebra?
(Fei Qi, September 21, 2016):
A meromorphic open string vertex algebra (MOSVA hereafter) is,
roughly speaking, a noncommutative generalization of a vertex algebra.
We hope that these algebras and representations will provide a
starting point for a new mathematical approach to the construction of
nonlinear sigma models in two dimensions.
Spring 2016
Noncommutative Poisson Geometry (Semeon Artamonov, April 27, 2016):
One of the major ideas of the noncommutative geometry program consists
of replacing the algebra of smooth functions on a manifold with some
general associative (not necessary commutative) algebra. It appears
that a lot of tools of conventional differential and algebraic
geometry can be translated to the noncommutative world. In my talk I
will focus on an implication of the noncommutative geometry program to
the Poisson manifolds.
Auslander-Reiten quivers of finite-dimensional algebras
(Rachel Levanger, March 9, 2016):
We summarize the construction of Auslander-Reiten quivers for
finite-dimensional algebras over an algebraically closed field.
We give an example in the category of commutative diagrams of
vector spaces.
Elliptic genera of singular varieties and related topics
(Lev Borisov, March 9, 2016):
A two-variable (Krichever-Hohn) elliptic genus is an invariant
of complex compact manifolds. It associates to such manifold $X$ a
function in two variables. I will describe the various properties of
elliptic genus. In particular, I will explain why it is a (weak) Jacobi
modular form if the canonical class of $X$ is numerically trivial. I will
then talk about extensions of the elliptic genus to some singular
varieties.
Relative Cartier divisors (Chuck Weibel, March 2, 2016):
If $B/A$ is a commutative ring extension, we consider the group
$I(B/A)$ of invertible $A$-submodules of $B$. If $A$ is a domain and
$B$ is its field of fractions, this is the usual Cartier divisor group.
The group $I(B[x]/A[x])$ has a very interesting structure, one which
is related to $K$-theory.
Arithmetic constructions of hyperbolic Kac-Moody groups
(Lisa Carbone, Feb. 17, 2016):
Tits defined Kac-Moody groups over commutative rings, providing
infinite dimensional analogues of the Chevalley-Demazure group
schemes. Tits' presentation can be simplified considerably when the
Dynkin diagram is hyperbolic and simply laced. In joint work with
Daniel Allcock, we have obtained finitely many generators and defining
relations for simply laced hyperbolic Kac-Moody groups over $\mathbb{Z}$. We
compare this presentation with a representation theoretic construction
of Kac-Moody groups over $\mathbb{Z}$. We also present some preliminary results
with Frank Wagner about uniqueness of representation theoretic
hyperbolic Kac-Moody groups.
Generalized adjoint actions (Volodia Retakh, Feb. 3, 2016:
We generalize the classical formula for expanding the
conjugation of $y$ by $\exp(x)$ by replacing $\exp(x)$ with any formal power
series. We also obtain combinatorial applications to $q$-exponentials,
$q$-binomials, and Hall-Littlewood polynomials.
(This is joint work with A. Berenstein from U. of Oregon.)
Symmetrization in tropical algebra (Louis Rowen, Jan. 21, 2015):
Tropicalization involves an ordered group, usually taken to be
$(\mathbb R, +)$ or $(\mathbb Q, +)$, viewed as a semifield.
Although there is a rich theory arising from this
viewpoint, idempotent semirings possess a restricted algebraic
structure theory, and also do not reflect important
valuation-theoretic properties, thereby forcing researchers to rely
often on combinatoric techniques.
A max-plus algebra not only lacks negation, but it is not even
additively cancellative. We introduce a general way to artificially
insert negation, similar to group completion. This leads
to the possibility of defining many auxiliary tropical structures,
such as Lie algebras and exterior algebras, and also providing a key
ingredient for a module theory that could enable one to use standard
tools such as homology.
Fall 2015
Representations of finite groups and applications
(Pham Huu Tiep, Dec. 7, 2015):
In the first part of the talk we will survey some recent results on
representations of finite groups. In the second part we will discuss
applications of these results to various problems in group theory,
number theory, and algebraic geometry.
Relative Cartier divisors and polynomials
(Charles Weibel, Nov. 11, 2015):
If A is a subring of a commutative ring B, a relative Cartier
divisor is an invertible A-submodule of B. These divisors form a group $I(A,B)$
related to the units and Picard groups of A and B. We decompose the
groups $I(A[t],B[t])$ and $I(A[t,1/t],B[t,1/t])$ and relate this
construction to the global sections of an étale sheaf.
This is joint work with Vivek Sadhu.
Automorphisms of extremal codes
(Gabriele Nebe, Nov. 4, 2015):
Extremal codes are self-dual binary codes with largest possible minimum
distance. In 1973 Neil Sloane published a short note asking whether there
is an extremal code of length 72. Since then many mathematicians search
for such a code, developing new tools to narrow down the structure of
its automorphism group. We now know that, if such a code exists,
then its automorphism group has order ≤5.
Noncommutative Cross Ratios
(Volodia Retakh, Oct. 28, 2015):
This is an introductory talk aimed at graduate students.
We will introduce cross ratios and use them to define a
noncommutative version of the Shear coordinates used in theoretical physics.
Quantization of Fock and Goncharov's canonical basis
(Dylan Allegratti, Oct. 21, 2015):
In a famous paper from 2003, Fock and Goncharov defined a version of the
space of $PGL_2(\mathbb C)$-local systems on a surface and showed that the
algebra of functions on this space has a canonical basis parametrized by
points of a dual moduli space. This algebra of functions can be canonically
quantized, and Fock and Goncharov conjectured that their canonical basis
could be deformed to a canonical set of elements of the quantized algebra.
In this talk, I will describe my recent work with Hyun Kyu Kim proving
Fock and Goncharov's conjecture.
Introduction to A-D-E singularities
(Lev Borisov, Oct. 14, 2015):
This is an introductory talk aimed at graduate students. ADE
singularities are remarkable mathematical objects which are studied from
multiple perspectives. They are indexed by the so-called Dynkin diagrams
$A_n$, $D_n$, $E_6$, $E_7$, $E_8$ and can be viewed as quotients of a
two-dimensional complex space $\mathbb C^2$ by a finite subgroup of the special
linear group $SL_2(\mathbb C)$. I will explain this correspondence as well as the
relationship between ADE singularities and the Platonic solids.
Monoids, monoid rings and monoid schemes
(Chuck Weibel, Oct. 7, 2015):
This is an introductory talk aimed at graduate students.
If $A$ is a pointed abelian monoid, we can talk about the topological
space of prime ideals in $A$, the monoid ring $k[A]$
and the topological space Spec(k[A]). Many of the theorems about
commutative rings have analogues for monoids, and just as schemes
are locally Spec(R), we can define monoid schemes.
I will explain some of the neaterr aspects of this dictionary.
Spring 2015
The Index Map and Reciprocity Laws for Contou-Carrère Symbols
(Jesse Wolfson, Feb. 4, 2015):
In the 1960s, Atiyah and Janich constructed a natural "index" map
from the space of Fredholm operators on Hilbert space to the
classifying space of topological K-theory. In joint work with Oliver
Braunling and Michael Groechenig, we construct an analogous index map
in algebraic K-theory. The index map allows us to relate the
Contou-Carrère symbol, a local analytic invariant of families of
schemes, to algebraic K-theory. Using this, we prove reciprocity laws
for Contou-Carrère symbols in all dimensions. This extends previous
results, of Anderson and Pablos Romo in dimension 1, and of Osipov and
Zhu, in dimension 2.
Zero divisors in the Grothendieck ring of varieties
(Lev Borisov, Feb. 25, 2015):
I will explain the motivation and results of my recent preprint
that shows that the class of the affine line is a zero divisor in the
Grothendieck ring of varieties.
Fall 2014
Semiclassical approximation to noncommutative Riemannian geometry
(Edwin Beggs, Sept. 17, 2014):
I will consider the first order deformation of a Riemannian manifold,
including the vector bundles, differential calculus and metric. One
example will be the Schwarzschild solution, which illustrates that not
all the properties of the classical case can be simply carried into
the quantum case. The other example is quantising the Kahler manifold,
complex projective space. This case is much simpler, and here the
complex geometry is also preserved. I will end with some comments on
the connection between noncommutative complex geometry and
noncommutative algebraic geometry.
Equivariant quantum cohomology and puzzles
(Anders Buch, Sept. 24, 2014):
The "classical equals quantum" theorem states that any equivariant
Gromov-Witten invariant (3 point, genus zero) of a Grassmann variety
can be expressed as a triple intersection of Schubert classes on a
two-step partial flag variety. An equivariant triple intersection on
a two-step flag variety can in turn be expressed as a sum over puzzles
that generalizes both Knutson and Tao's puzzle rule for Grassmannians
and the cohomological puzzle rule for two-step flag varieties. These
results together give a Littlewood-Richardson rule for the equivariant
quantum cohomology of Grassmannians. I will speak about geometric and
combinatorial aspects of this story, which is based on papers with
Kresch, Purbhoo, Mihalcea, and Tamvakis.
Cut and paste approaches to rationality of cubic fourfolds
(Lev Borisov, Oct. 8, 2014):
A random 4-dimensional hypersurface of degree 3 is widely
expected to be nonrational, but no proof of this statement currently
exists. Moreover, there is no clear understanding precisely which such
fourfolds are ratonal. An approach to this problem developed in a recent
preprint of Galkin and Shinder gives an unexpected necessary condition of
rationality modulo a variant of cancellation conjecture. This is a
surprisingly short and clean argument that involves the Grothendieck ring
of varieties. I will aim to make my talk accessible to the audience with
very limited algebraic geometry background.
The Witt group of real varieties (Chuck Weibel, Oct. 15, 2014):
We approximate the Witt groups of a variety V over the reals,
using a topological invariant: the Witt groups
of Real vector bundles on the space of complex points of V.
This is a better approximation than one might expect, and
has the advantage of being finitely generated.
This is joint work with Max Karoubi.
Jacobians of modular curves (Ed Karasiewicz, Oct. 22, 2014):
We study the Jacobian variety of a modular curve $C$
over an elliptic curve, and its Hecke operators.
The goal is to show that the $L$-function of a weight 2 cusp form
for $C$ is the same as the $L$-function of the elliptic curve.
A Modular Operad of Embedded Curves (Charles Siegel, Oct. 29, 2014):
Modular operads were introduced by Getzler and Kapranov to formalize the
structure of gluing maps between moduli of stable marked curves. We present
a construction of analogous gluing maps between moduli of
pluri-log-canonically embedded marked curves, which fit together to give
a modular operad of embedded curves.
This is joint work with Satoshi Kondo and Jesse Wolfson.
Some non-compact Riemann surfaces branched over three points
(Marvin Tretkoff, Nov. 12, 2014):
Recall that the Riemann surface of the multi-valued function
$\log(z)$ is an infinite sheeted covering of the z-sphere branched over the
two points $z=0$ and $z=\infty$ and has an ''infinite spiral ramp'' over
each of them. Consequently, its monodromy group is infinite cyclic.
Today, we construct Riemann surfaces as infinite sheeted coverings of the
z-sphere that are branched over precisely three points on the z-sphere.
Moreover, each of these Riemann surfaces has a single ''infinite spiral
ramp'' over each of its branch points. The monodromy groups of such surfaces
are infinite two generator groups of permutations of the set of integers.
Our construction yields many non-isomorphic groups with varying algebraic
properties. In this lecture, we shall discuss one of these in some detail.
Property T for Kac-Moody groups (Ashley Rall, Nov. 19, 2014):
I will give a brief introduction to Kac-Moody groups, infinite dimensional
analogues of Chevalley groups, and Kazhdan's property (T) and then discuss
joint work with Mikhail Ershov establishing property (T) for Kac-Moody groups
over rings. We expand upon previous results by Dymara and Januszkiewicz
establishing property (T) for Kac-Moody groups over finite fields and by
Ershov, Jaikin, & Kassabov establishing property (T) for Chevalley groups
over commutative rings to prove that given any indecomposable 2-spherical
generalized Cartan matrix A there is an integer m (depending solely on A)
such that if R is a finitely generated commutative unital ring with no
ideals of index less than m then the Kac-Moody group over R associated
to A property (T).
Sieve methods in group theory (Alex Lubotsky, Dec. 3, 2014):
The sieve methods are classical methods in number theory.
Inspired by the 'affine sieve method' developed by Sarnak, Bourgain,
Gamburd and others, as well as by works of Rivin and Kowalsky, we develop
in a systemtic way a 'sieve method' for group theory. This method is
especially useful for groups with 'property tau'. Hence the recent results
of Breuillard-Green-Tao, Pyber-Szabo, Varju and Salehi-Golsefidy are
very useful and enables one to apply them for linear groups.
We will present the method and some of its applications to linear
groups and to the mapping class groups.
[Based on joint with Chen Meiri (JAMS) and with Lior Rosenzweig (to
appear in Amer. J. of Math.) ].
Fall 2013
Torsion Theory and Slice Filtration of Homotopy Invariant
Sheaves With Transfers
(Knight Fu, Sept. 16, 2013):
Torsion Theory makes important contributions to the study of modules
over a ring. It also plays an important role in constructing the
quotient of an abelian category by a "torsion" subcategory.
Applying
torsion theory to the category of homotopy invariant sheaves with
transfers, we show how a sequence of co-radical functors gives rise to
two filtrations --- one increasing, one decreasing --- of the
category. We conjecture that the obtained structure ought to be the
"slice filtration" on the category, and show how the filtrations are
compatible with the slice filtration on Voevodsky's derived category
of motives.
Spring 2013
Equations, syzygies, and vector bundles
(Daniel Erman, Jan. 24, 2013):
For a system of polynomial equations, it has long been
known that the relations (or syzygies) among the polynomials provide
geometric information about the corresponding projective variety. I
will describe a collection of new ideas about how to study syzygies,
and how these lead to classification results and a duality between
syzygies and vector bundles.
Equivariant Schubert calculus: positivity, formulas, applications
(David Anderson, Jan. 30, 2013):
Schubert's enumerative calculus is the subject of Hilbert's 15th
problem. It is a technique for solving problems of enumerative geometry;
for example, how many conics are tangent to five given conics? In its
modern formulation, Schubert calculus concerns computations in the
cohomology rings of Grassmannians, flag varieties, and related spaces.
These spaces carry large group actions, which can be used to both
refine and simplify the computations. The cohomology calculations can
be modeled by multiplication of polynomials, and a central role is
played by these polynomial representatives. Formulas for these
polynomials are of both theoretical and computational interest.
In this talk, I will survey recent developments in this subject,
including some new formulas and applications.
What is a Derivator? (Chuck Weibel, Feb. 6, 2013):
As the name implies, this is an introductory talk.
Derivators were introduced in 1983 by Grothendieck in a 600-page manuscript,
and refined in his 2000-page manuscript in 1991. They are designed to
enhance triangulated categories, and have recently been used in the study
of non-commutative algebraic geometry.
A geometric approach to noncommutative Laurent phenomenon
(V. Retakh, Feb. 13, 2013):
A composition of birational maps given by Laurent polynomials need not be
a Laurent polynomial. When it does, we talk about the Laurent
phenomenon. A large variety of examples of the Laurent phenomena for
commuting variables comes from the theory of cluster algebras. Much
less is known in the noncommutative case. I will present a number of the
noncommutative Laurent phenomenoma of a "geometric origin." This is a
joint work with A. Berenstein.
Dynamics and surjectivity of some word maps on SL(2,q)
Tatiana Bandman, Feb. 20, 2013):
I will speak about a geometric approach, based on the
classical trace map, for investigating dynamics, surjectivity and
equidistribution of word maps on groups PSL(2,q) and SL(2,q).
It was also used for a characterization of finite solvable groups
by two-variable identities.
Strongly Dense Subgroups of Algebraic Groups
(Robert Guralnick, Feb. 27, 2013):
Let G be a simple algebraic group. A free finitely generated
subgroup H of G is called strongly dense in G if every nonabelian
subgroup of H is Zariski dense in G. We will discuss joint work
with Breuillard, Green and Tao which shows that strongly dense
subgroups exist (over sufficiently large fields) and some recent
improvements on this by Brueillard, Guralnick and Larsen.
This has applications to finding Cayley graphs of finite simple
groups of Lie type and some results on generation of finite
simple groups of Lie type. Using these ideas, we can also
improve on results of Borel and Deligne-Sullivan related to
the Hausdorff-Banach-Tarski paradox.
The 3 main problems in the braid group
(Mina Teicher, March 13, 2013):
These are: The Word Problem, The Conjugacy Problem and the
Hurwitz Equivalence Problem. I shall present the questions,
some answers and, time permitted, also an application to Cryptography.
Intersection theory on singular varieties
(Joe Ross, April 3, 2013):
Whereas algebraic cycle classes may be multiplied on a smooth variety,
this is not in general possible on a singular variety. In topology,
the intersection homology groups of Goresky-MacPherson provide
interesting invariants of singular spaces. Intersection homology sits
in between singular cohomology and homology, and admits natural
pairings generalizing the product structure on the singular homology
of a smooth manifold.
I will propose an algebraic analogue of intersection homology which
sits in between the algebraic cocycles of Friedlander-Lawson and the
classical Chow groups. In some special cases these "intersection Chow
groups" admit pairings. This is joint work with Eric Friedlander.
On Hilbert modular threefolds of discriminant 49
(Lev Borisov, April 10, 2013):
I will talk about joint work with Paul Gunnells in which we
explicitly describe a certain Hilbert modular threefold as a hypersurface
in a weighted projective space. As a byproduct we find an octic surface in
P^3 with 84 singularities of type A_2.
Implicit systems of differential equations
(Freya Pritchard, April 24, 2013)
We will consider implicit systems that are given by polynomial
relations on the coordinates of the indeterminate function and the
coordinates of the time derivative of the indeterminate function. For such
implicit system of differential-algebraic equations, we will be concerned
with algebraic constraints such that on the algebraic variety determined by
the constraint equations the original implicit system of differential
equations has an explicit representation.
Our approach to such systems is algebraic. Although there have been a
number of articles that approach implicit differential equations
algebraically, all such approaches have relied heavily on linear algebra.
The approach that we will consider is different in that we have no
linearity requirements at all, instead we shall rely on classical algebraic
geometry. In particular we will use birational mappings to produce an
explicit system of differential equations and an algebraic variety of
possible initial values.
Structure of Chevalley groups over rings
(Alexei Stepanov, May 1, 2013)
Let G be a Chevalley group scheme with elementary group E.
Using a localization procedure to reduce to the well understood
case of local rings,
we study the following problems over a commutative ring R:
a) Normality of E(R) and commutator formulas;
b) Nilpotent structure of K1=G(R)/E(R)
c) bounded word length in E(R); and
d) normal subgroups of G(R).
Fall 2012
Given a generalized flag manifold X = G/P, a Schubert variety X(w),
and a degree d, consider the set of points that can be reached from
X(w) by a rational curve of degree d, i.e. the union of all rational
degree d curves through X(w). It turns out that the Zariski closure
of this set is a larger Schubert variety, which is important for many
aspects of the quantum cohomology of X, including the quantum
Chevalley formula and the smallest q-degree in the quantum product of
two Schubert classes. I will give a very explicit description of this
"curve neighborhood" of the Schubert variety in terms of the Hecke
product of Weyl group elements, and use it to give a simple proof of
the (equivariant) quantum Chevalley formula. This is joint work with
Leonardo Mihalcea.
This is joint work with Alexandra Seceleanu and Michael E. Stillman.
We describe Groebner bases for the ideals of relations between the
Chern classes of the tautological bundles on partial flag bundles,
and show how the result can be used to enable practical computation
of intersection numbers in the "Macaulay2" package "Schubert2".
We also generalize the result to cover isotropic flag bundles.
Let F be a perfect field of characteristic different from 2. In joint
work with Paul Arne Ostvaer, we describe the slices of hermitian K-theory
and higher Witt-theory in the motivic stable homotopy category of F.
Applications include computations of hermitian K-groups and Witt groups
for number fields and projective spaces, as well as a different perspective on
Milnor's conjecture on quadratic forms.
The first term of Gersten conjecture for K-theory claims the injectivity
of the map K_i(R)→K_i(K) for any regular semilocal ring R with field
of fractions K. The same statement with K_i replaced by the etale
cohomology functor H^1(-,G), where G a reductive algebraic group,
is known as the Grothendieck-Serre conjecture. The latter conjecture was
recently settled by I. Panin et al. under the assumption that R contains
an infinite perfect field. We discuss how essentially the same argument
carries over to non-stable K_1 and similar functors.
Spring 2012
Deformation quantization is a procedure which
assigns a formal deformation of the associative algebra of
functions on a variety to a Poisson structure on this variety.
Such a procedure can be obtained from Kontsevich's
formality quasi-isomorphism and, it is known that, there are
many homotopy inequivalent formality quasi-isomorphisms.
I propose a framework in which all homotopy classes of
formality quasi-isomorphisms can be described. More precisely,
I will show that homotopy classes of "stable" formality quasi-isomorphisms
form a torsor for the group exp(H°(GC)), where GC denotes
the full graph complex. The group exp(H°(GC)) is isomorphic
to the Grothendieck-Teichmueller group which is, in turn, related to
moduli of curves and to theory of motives.
Shift equivalence is an equivalence relation on nxn matrices (say over Z).
Such a matrix T may be regarded as defining a Z[t]-module structure on a
free abelian group, and shift equivalence translates into the assertion that
the modules become isomorphic over Z[t,1/t]. This talk is a description of
a weaker equivalence relation related to class groups of number fields.
Thomas and Yong have conjectured a Littlewood-Richardson
rule for the K-theory of any minuscule homogeneous space, based on
counting tableaux that rectify to a certain superstandard tableau.
This conjecture has been proved for Grassmannians of type A and
maximal orthogonal Grassmannians, but it fails for the Freudenthal
variety of type E7. I will speak about a fix that replaces the
superstandard tableaux with minimal increasing tableaux. These
tableaux have several other combinatorial advantages, for example they
make it possible to recognize which tableaux should be counted without
rectifying them. This is joint work with Matthew Samuel.
(Julia Plavnik, February 29, 2012):
A good way of thinking about category theory is that it is a
refinement (or "categorification") of ordinary algebra. In other
words, there is a dictionary between these two subjects, such
that usual algebraic structures are recovered from the corresponding
categorical structures by passing to the set of isomorphism classes
of objects (Etingof, Gelaki, Nikshych and Ostrik).
Given, for example, a polynomial $f(x_1,...,x_n)$ with
complex coefficients, a matrix factorization of f is a pair of r x r
matrices of polynomials (A, B) satisfying $AB = f I_r = BA$. Introduced
over 30 years ago by Eisenbud in the context of studying projective
resolutions of modules over hyper-surfaces, there has been a revival
of interest in matrix factorizations lately, as connections with
mathematical physics and knot theory have emerged. I will discuss some
recent progress in understanding certain fundamental invariants of
matrix factorizations.
I will review the combinatorial aspects of toric mirror
symmetry. In particular, I will focus on the new phenomena one encounters
when dealing with complete intersections as opposed to hypersurfaces.
I will discuss the Laurent phenomenon for noncommuting variables.
A good example is the cluster conjecture of Kontsevich. I will present
a proof of the conjecture, recently obtained by A. Berenstein and me.
(Ben Wyser, April 18, 2012:
Suppose that G is one of the classical groups SL(n,C), SO(n,C) or Sp(2n,C),
and that K is a symmetric subgroup of G --- that
is, the fixed points of an involution of G. The group K has finitely
many orbits on the flag variety G/B, and the geometry of these orbits
and their closures is closely connected to the theory of Harish-Chandra
modules for a certain real form of G. Their representation-theoretic
interest aside, such orbit closures are, in a sense, generalizations of
Schubert varieties, and most questions one has about Schubert varieties
can equally well be posed about these more general objects.
Fall 2011
The relationship between algebraic curves and abelian varieties has a long
and classical history. One of the most fundamental open problems is
determining when an abelian variety is the Jacobian of some curve. We will
discuss some of the history of the problem, as well as new results in the
case of genus 5 curves.
(Abid Ali, Sept. 28, 2011):
Let G be a complete Kac-Moody group of rank 2 over a finite field, and
let B— denote the non-uniform lattice subgroup generated by the
"diagonal subgroup" and all negative real root groups. We define
and construct congruence subgroups of B—.
This is joint work with Lisa Carbone.
(Raika Dehy, October 4 and 18, 2011):
This talk is motivated by the representation-theoretic approach to
Fomin-Zelevinsky's cluster algebras. In this approach a central role
is played by certain 2-Calabi-Yau categories and by combinatorial
invariants associated with their rigid objects (objects with no
self-extensions).
Let X be an orthogonal Grassmannian, defined as the set of all
isotropic subspaces of a given dimension in a complex vector space
equipped with an orthogonal bilinear form. The cohomology ring H^*(X)
has a basis consisting of Schubert classes; products of these classes
have applications in enumerative geometry and are the main objects of
study in Schubert calculus. The cohomology ring H^*(X) can also be
understood in terms of generators and relations, where the generators
are certain special Schubert classes. A Giambelli formula means an
expression of an arbitrary Schubert class as a polynomial in special
Schubert classes. The Schubert classes of an ordinary Grassmann
variety can be expressed as determinants of matrices of special
Schubert classes, and the Schubert classes of a maximal orthogonal
Grassmannian can be written as Pfaffians. I will speak about new
Giambelli formulas for submaximal orthogonal Grassmannians that is
expressed in terms of raising operators and interpolate between the
above cases. This is joint work with A. Kresch and H. Tamvakis.
Orlov showed in 1997 that all exact, fully faithful functors between
the bounded derived categories of two smooth projective varieties are
isomorphic to a Fourier-Mukai transform. In this talk we will discuss
a class of functors that are not full or faithful and still satisfy
the above result.
In this talk I will introduce four dualizing complexes defined by
M. Spiess, T. Moser, S. Bloch (duality proved by T. Geisser) and K. Sato,
and compare them in the derived category. We show that Bloch's complex is
quasi-isomorphic with all three, in the situation when they are properly
defined (and assuming some well-known conjectures).
Algebraic Topology and Algebraic Geometry throughout the years have
shared common methods and enriched each other. The work of
Morel-Voevodsky gives a natural categorical framework to import some
standard methods from homotopy theory into algebraic geometry. The
aim of this talk is to describe some concrete examples.
Spring 2011
Let p1,...,pk be a collection of points with integer
coordinates. Denote their convex hull by Δ. For every integer n
consider the subset inside the multiple nΔ which consists of
lattice points that can be written as sums of n of the pi.
Typically, some lattice points of nΔ will be missing from this set.
The toric Eisenbud-Goto conjecture gives a certain measure of control
over the sets of missing points. I will give an elementary introduction to the
conjecture, which is still open for the case of six points on the plane.
(Crichton Ogle, April 13, 2011):
Using techniques developed for studying polynomially bounded cohomology, we
show that the assembly map for K*t(l¹(G)) is
rationally injective for all finitely presented discrete groups G.
This verifies the l¹-analogue of the Strong Novikov Conjecture for
such groups. The same methods show that the Strong Novikov Conjecture for
all finitely presented groups can be reduced to proving a certain
(conjectural) rigidity of the topological cyclic chain complex
CC*t(HCM(F)) where
F is a finitely-generated free group and
HCM(F) is the "maximal" Connes-Moscovici algebra
associated to F.
A system of polynomial equations over a field F may have
solutions in a collection of finite field extensions of relatively prime
degree, but not have any solution in F. We will describe some examples and
results known about this phenomenon, and then talk about what A^1-homotopy
theory might contribute to understanding it.
Fall 2010
In the late 1990s, Lunts and Rosenberg gave a definition of quantum
differential operators on graded algebras which allow us to view the
action of quantum groups on graded algebras as quantum differential
operators. We present the algebras of quantum differential operators
on certain graded algebras.
The prime ideals in an abelian monoid are the points of a topological space,
and we can glue them together to get finite models of toric varieties and other
objects in algebraic geometry. In this introductory talk, we give basic
properties of these monoidal schemes, such as normalization,
proper maps and resolution of singularities.
Sizes of fixed point spaces for elements in linear groups have a long
history. These types of results include the classification of
psuedoreflection groups and Frobenius complements. I will talk about
recent joint works with Maroti and Malle which answer two conjectures
from Peter Neumann's 1966 thesis. The first conjecture has to do with
the average dimension of a fixed space of an element in a finite
(irreducible) linear group. The second has to do with the minimal
dimension of a fixed space of some element in an irreducible (possibly
infinite) linear group.
In topology, the Steenrod algebra describes all natural transformations
between cohomology groups H*(-,Z/p). Modifying this construction,
Epstein constructed certain operations Pi on etale cohomology
with coefficients Z/p, used by Raynaud in her construction of universal
projective modules. We modify his construction to allow twisted coefficients
such as μp, and give a complete list of all etale cohomology
operations in this context.
This is joint work with Bert Guillou.
The K-theoretic Schubert structure constants of a homogeneous space
G/P are known to have signs that alternate with codimension by a
result of Brion. For Grassmannians of type A, these constants are
computed by a generalization of the classical Littlewood-Richardson
rule that counts set-valued tableaux. The K-theory ring of any
Grassmann variety is generated by special Schubert classes that
correspond to partitions with a single row.
Let k be a field of characteristic zero. The simple Lie algebra
W1=Der k[x], the one-sided Witt algebra, has a basis
ei=x(i+1)d/dx for i at least -1.
The wedges of e0 and ei satisfy the classical
Yang-Baxter equation, giving W1 the structure of a coboundary
triangular Lie bialgebra. Its continuous Lie dual is also a Lie bialgebra,
and has been identied with the space of k-linearly recursive sequences by
W. Nichols.
Let f=(fn) and g=(gn) be linearly recursive sequences
in the continuous linear dual. For each n, the n-th coordinate of [f,g]
has been described in terms of the coordinates of f and of g, but it was
an open problem to give a recursive relation satised by [f,g] in terms
of recursive relations satisfied by f and by g. We give such a relation here.
Analogous`results hold for the two-sided Witt algebra Der k[x,x-1].
This is joint work with Zhifeng Hao.
Voevodsky gave a description of all stable operations in motivic cohomology
in 2009. However, many other unstable operations have come to light
in the last decade. We determine the unstable operations.
This is joint work with Bert Guillou.
There are certain classic algebraic structures like
Gerstenhaber's bracket which have their origin in operads. We discuss
several generalizations of these structures - notably Lie brackets, BV
operators and master equations. We show how these appear naturally in
operadic settings. Our general theory gives a unified framework for a
diverse set of geometric and algebraic examples.
Spring 2010
This is joint work with Jon Berrick and Paul Arne Ostvaer.
It has been known for a few years,
essentially by the work of Voevodsky and Rost,
that the algebraic K-theory of a commutative
ring A with finite coefficients is periodic above
the etale cohomological dimension of A. In this lecture,
we show that such a ring A
has also a periodic hermitian K-theory in the same range.
This essentially means that theorems about the general (infinite) linear
group, such as the one proved by Rost and Voevodsky,
imply similar ones for the orthogonal and symplectic groups.
Basic properties of stable bundles on a projective, smooth
variety X will be outlined. These properties make maps between stable
bundles quite rigid so that such bundles behave almost like elements in a
basis of a vector space over a field. The picture is particularly clear for
projective, smooth varieties over a finite field. This will be applied to
determine generators of the Witt group of X and to show that the stable
Brauer group of X is the same as the Brauer group of X.
Familiarity with the definitions of Witt groups and Brauer groups of
fields will be helpful but not essential.
Drinfeld twists were introduced by Drinfeld in his work on
quasi-Hopf algebras. In joint work with Pierre Guillot
(arXiv:0903.2807, published in IRMN), after observing that the
invariant Drinfeld twists on a Hopf algebra form a group, we determine
this group when the Hopf algebra is the algebra of a finite group G.
The answer involves the group of class-preserving outer automorphisms
of G as well as all abelian normal subgroups of G of central type.
Linearly recursive sequences have a bialgebra structure.
Polynomially recursive(or D-finite) sequences have a topological
bialgebra structure. If such a sequence is of a combinatorial nature,
a formula for its coproduct can often be interpreted as a combinatorial
identity. We illustrate this for the sequences whose n-th term is
((ni)(n!)) for a fixed non-negative i, where
(ni) is the binomial coefficient. The resulting
combinatorial identity is of an iterated Vandermonde type.
This is an overview of the notion of tilting, from Gelfand-Ponomarev
to the 1990s. Given a ring A, an A-module T is tilting if
it has finite projective dimension, Exti(T,T)=0 for i>0,
and there is a resolution
0 → A → T0 → ... → Tn →0
with the Ti summands of sums of copies of T.
Then Hom(T,-) and T⊗B- determine an equivalence
between Db(A) and Db(B), where B=End(T).
In the associated torsion theory, the torsion modules are
the quotients of direct sums of copies of T.
Tilting modules were introduced in the 1970s (originally by Gelfand-Ponomarev
to construct reflection functors), with the restriction that the modules have
projective dimension 1. We will present the main results of tilting in this
setting, including the torsion theory associated with these modules.
The modern notion of a tilting module was presented in the seminar talk
Tilting 1, and is due to Cline-Parshall-Scott. Any left derived
functor inducing an equivalence between A-modules and B-modules
arises from a tilting module, as RHom_A(T,-).
Let k be a field of characteristic p>0. We consider monic linear
homogeneous differential equations (LHDE) over the ring of Hurwitz series
Hk of k. We obtain explicit recursive expressions for solutions of
such equations and show that Hk admits a full a set of solutions as
well. We then consider the notion of intertwining of Hurwitz series to
reduce the study of solutions of an nth order equation to
a system of n first order equations in a particularly simple form.
For every LDHE over Hk we will associate a module
(over a suitable quasifield extension of k), which is closed under
the shift derivation of Hk and discuss the structure of the
group of module automorphisms that commutes with the shift derivation.
Fall 2009
A differential field is a field K with a derivation, that is,
an additive map D:K → K satisfying D(fg)=D(f)g+fD(g)
for f,g in K. The field of constants C of K are the zeros of D.
A differential central simple algebra (DCSA) over K is a pair
(A,\mathcal D) where A is a central simple algebra and $\mathcal D$
is a derivation of A extending the derivation D of its center.
Any DCSA, and in particular a matrix differential algebra over K,
can be trivialized by a Picard-Vessiot (differential Galois) extension
E of K. In the matrix algebra case, there is a correspondence between
K-algebras trivialized by E and representations of the differential
Galois group of E over K in PGLn(C) that can be
interpreted as cocycles equivalent up to coboundaries. I will start with
a brief introduction to differential Galois theory.
A permutation on a set is called a derangement if it has
no fixed points. The study of the proportion of derangements
in finite transitive groups has a long history and the problem has
many applications. We will discuss this as well as the analogous
problem for algebraic and show the connection between the two.
In particular, we will discuss recent results (joint with Fulman)
about conjugacy classes in finite Chevalley groups and the solution
of a conjecture made independently by Aner Shalev and Nigel Boston.
Frobenius invented group character theory in order to solve
the problem of the factorization of the group determinant. His papers
are hard to understand and when the modern methods for group
representation theory were introduced his initial work was largely
forgotten. To each representation of a (finite) group there is
associated a polynomial which is a factor of the group determinant,
and Frobenius introduced "k-characters" to describe this
polynomial. Professor Gelfand has commented that perhaps physicists
might benefit from looking at these polynomials. Among other places
these k-characters have occurred in work of Buchstaber and Rees and
also are related to work of Wiles and Taylor on
"pseudocharacters" of finite dimensional representations of
infinite groups.
I will describe the early work from an elementary
point of view and give an account of some of the new ideas coming from
it, and also indicate some of the connections with probablity.
(Chloe Perin, Nov. 2, 2009):
Let C be a cyclic subgroup of a finitely generated free group F. We
show that the intersection of a definable set D in F^n with C^n is in
the Boolean algebra of cosets of subgroups of C^n. In other words, the
definable structure induced by the embedding of C in F is no richer
than the definable structure on C. We make extensive use of Sela's
geometric techniques for studying the first-order theory of the free
group, in particular of his construction of "formal solutions" to an
equation.
An unperforated partially ordered abelian group A is a
dimension group if A satises the Riesz interpolation property
(given a,a' ≤b,b' there is a c with a,a' ≤ c ≤b,b').
These are related to "Bratteli diagrams". Paul will discuss
the difficulty of classifying them when the rank is at least 3,
and show that the problem for a given rank cannot be reduced to the
classification problem for a smaller rank.
Let F be a characteristic zero differential field with an
algebraically closed field of constants C. I will describe the construction
of a Picard-Vessiot Extension (PVE) for a linear homogeneous
differential equation over F. The group of differential automorphisms
of a PVE fixing F is called the differential Galois group;
there is a Galois correspondence between its algebraic subgroups
and intermediate differential subfields. Examples of PVEs for F=C(x)
with the usual derivation will be discussed, and we will also compute
the differential Galois group for our examples.
Spring 2009
This is an introductory survey talk.
There is a complex topological manifold, called the Stability Space,
associated to any triangulated category D. It was conceived by Mike
Douglass as an aspect of string theory, and made mathematical by
Tom Bridgeland. Subspaces correspond to t-structures, and the stability
space of the projective line is the affine complex plane.
A differential quasifield is a natural generalization of a differential
field in characteristic p>0. Elementary properties of
differential quasifields are considered, and a generalized version
of the theorem on the connection between linear independence over
constants and the Wronskian is presented.
In a recent seminar (2/2/09), C. Weibel discussed recent developments on
stability in (triangulated) categories. These developments are inspired by
physics, in particular string theory. This introductory talk will explain
the notion of stability in string theory, and how it is connected to
stability in mathematics.
The Nekrasov conjecture predicts a relation between the partition
function for N=2 supersymmetric Yang-Mills theory and the Seiberg-Witten
prepotential. For instantons on ℝ4, the conjecture
was proved, independently and using different methods, by Nekrasov-Okounkov,
Nakajima-Yoshioka, and Braverman-Etingof. We prove a generalized version of
the conjecture for instantons on noncompact toric surfaces.
In a recent seminar (2/23), Leon Pritchard talked about partitioned
differential quasifields.
(Chris Woodward, April 20, 2009):
I will talk about a "quantum non-abelian localization" conjecture that
relates Gromov-Witten invariants of GIT quotients with equivariant
Gromov-Witten invariants of the total space. Some special cases are
proved. A key notion in the conjecture is the notion of morphism of
cohomological field theories, which "complexifies" the notion of
A-infinity morphism.
We will explain how one can define Hochschild (co)chain complex
associated in a functorial way to any space X, CDG algebra A and
A-module M. We will give several examples and applications to Adams
operations and (if time permits) Brane topology.
Fall 2008
Notation: k denotes a unital algebra over the complex numbers which is
commutative, finitely generated, and nilpotent-free,
i.e., k is the coordinate algebra of a complex affine variety. A
k-algebra is an algebra A over the complex numbers
which is a k-module such that the algebra structure and the k-module
structure are compatible in the evident way.
Note that A is not required to be commutative. Prim(A) denotes the
set of primitive ideals in A. Prim(A) is topologized
by the Jacobson topology.
The above is joint work with A.M.Aubert and R.J.Plymen.
I will start my talk with a review of the algebraic
operations on the pair Hochschild cochain complex
and Hochschild chain complex of an associative algebra.
Then I will speak about the formality theorems
for these complexes. Finally I will discuss applications
of these formality theorems to deformation quantization,
computation of Hochschild (co)homology and
the Kashiwara-Vergne conjecture.
I will present various results about the arithmetic of dynamical systems
given by iterating a polynomial mapping over a ring. Sample topics
include: describing the minimal N for which the backward orbit of a point
under a given polynomial over a number field K contains infinitely many
points of degree N over K; and determining the possible lengths of
periodic and preperiodic forward orbits of a point under a polynomial
mapping of a ring. I will also discuss connections with torsion in
abelian varieties, Sen's theorem (Grothendieck's H^1 conjecture), and the
Nottingham group.
R. G. Larson and E. J. Taft showed that the space of linearly
recursive sequences is a bialgebra. A coproduct formula for such a
sequence can be interpreted as a quadratic identity on the coordinates
of the sequence. This was extended by C. A. Futia, E. F. Mueller and
E. J. Taft[CMT] to D-finite sequences. This means that from some point
on, each coordinate is a linear combination of previous coordinates
with variable(polynomial) coefficients. These D-finite sequences form a
topological bialgebra, i.e., the coproduct is an infinite sum of tensor
products of such sequences. Such a coproduct formula can still be
interpreted as a quadratic identity on the coordinates, often of a
combinatorial nature. In [FMT], we obtained such formulae and
identities for the sequences (n!) and (n(n!)). Here we extend this to
the sequences whose n-th term is ((n/k)(n!)) for each k=2, 3, 4,....
Here (n/k) is the binomial coefficient.
Let G be a locally compact Kac-Moody group of affine or hyperbolic type
over a finite field Fq; G admits an action on its
Tits building X. In the setting rank(G)=2, X is a locally finite,
homogeneous tree. We can then use the combinatorial tools of
Bass-Serre theory, namely graphs of groups, to construct discrete
subgroups of G. We show that if q=2 then G contains a cocompact lattice
Γ whose quotient Γ\X equals G\X, a simplex. We then give
two distinct constructions of infinite towers
Given a quiver Q and a field k, it is possible to associate several
k-algebras. Best known among them is the path algebra, PQ.
Localizing PQ one obtains a new algebra, the Leavitt algebra LQ.
This algebra is equipped with an involution. If k is the field of
complex numbers, LQ may be view as an algebra of operators in Hilbert
space; its completion in the operator norm gives a C*-algebra, the
Cuntz-Krieger algebra of the quiver. The topological K-theory of the
Cuntz-Krieger algebra was computed in a now classical paper of Cuntz.
In the talk we will discuss recent joint results with Pere Ara and
Miquel Brustenga concerning the algebraic K-theory of LQ and its
relation with the topological K-theory of the Cuntz-Krieger algebra.
Spring 2008
I will discuss a conjectural relationship between certain quantum
W-algebras (vertex algebras) and finite-dimensional quantum groups
associated to $sl_2$ (Hopf algebras). In the process we shall
encounter interesting multisum identities.
I will present various results about the lattice of fields between K and K(x),
where K is a field. These include classical results of Ritt, Schinzel,
Fried, et al., as well as new results. I will also give some applications,
for instance a recent joint result with Ghioca and Tucker describing all
pairs of complex polynomials having orbits with infinite intersection.
Symbolic dynamics is a standard and powerful tool to understand
chaotic dynamics. For example, we can identify the Julia set of
quadratic polynomials with the one-sided shift space, the space
of infinite sequences of 0 or 1, provided the parameter of the
map is outside the Mandelbrot set. Furthermore, via the monodromy
homomorphism, the topological structure of the Mandelbrot set is
also captured by the automorphism group of the shift space.
Hurwitz proved that a complex curve of
genus g>1 has at most 84(g-1) automorphisms.
In case equality holds, the automorphism group
has a quite special structure. However, in a
qualitative sense, all finite groups G behave the
same way: the least g>1 for which G acts on a
genus-g curve is on the order of (#G)*d(G), where
d(G) is the minimal number of generators of G.
I will present joint work with Bob Guralnick on
the analogous question in positive characteristic.
In this situation, certain special families of
groups behave fundamentally differently from
others. If we restrict to G-actions on curves
with ordinary Jacobians, we obtain a precise
description of the exceptional groups and curves.
Quillen invented the notion of a model category in order to do
homotopical algebra. We will consider these structures on the categories
of R-modules, presheaves and sheaves, and show how localization works.
We discuss the following open concerning rational points
on homogeneous spaces under connected linear algebraic groups.
If a homogeneous space under a connected linear algebraic group
has a zero cycle of degree one, does it admit a rational point?
We explain the arithmetic case and some recent progress
concerning this question for more general fields.
(Tom Robinson, March 14, 2008):
First I will show explicitly how a calculation in
Frenkel-Lepowsky-Meurman's book on vertex operator algebras, which I
will in its essentials redo, can be viewed as an application of a
formal representation of exponentiated derivations. The outcome of
the calculation is Faa di Bruno's formula for the higher derivatives
of a composite function. Then building on this result I will show how
another application of an easy class of formal differential
representation leads to the Riordan Group. No prerequisites
necessary.
I will explain current joint work with David Nadler, in which the
representation theory of real reductive Lie groups is examined through
the lens of topological field theory and the geometric Langlands
program. Our main results show how to recover the representation
theory of real forms of a complex group G from the representation
theory of G, and how to deduce a Langlands dual description of the
representation theory (a form of Soergel's conjecture, generalizing
results of Vogan and Langlands).