## RUTGERS ALGEBRA SEMINAR - Fall 2018 (Wednesdays at 2:00 in H525)

The Algebra Seminar meets on Wednesdays, at 2:00-3:00PM in room H525
(in the Hill Center, on Busch Campus of Rutgers University).
A more comprehensive listing of all Math Department seminars is available.
Here is a link to the algebra seminars in previous semesters

Fall 2018 Seminars (Wednesdays at 2:00 in H525)

19 Sep Nicola Tarasca  Rutgers  "Geometry and Combinatorics of moduli spaces of curves"
26 Sep Angela Gibney  Rutgers  "Basepoint free loci on $M_{0,n}$-bar from Gromov-Witten theory of smooth homogeneous varieties"
5 Oct(FRI) Michael Larsen Indiana U  TBA
*** Friday at 10:00 AM in Hill 005 ***
10 Oct Yotam Hendel  Weizmann Inst. "On singularity properties of convolutions of algebraic morphisms"
17 Oct
24 Oct Sandra Di Rocco KTH-Sweden     "Algebraic Sampling"
31 Oct Igor Rapinchuk  Michigan State "finiteness results in étale cohomology"
7 Nov
14 Nov
21 Nov --- no seminar ---      Thanksgiving is Nov. 22; Friday class schedule
28 Nov Julie Bergner  U.Virginia  TBA (2-Segal categories?)
5 Dec
12 Dec Patrick Brosnan  U.Maryland "Palindromicity and the local invariant cycle theorem"

Classes end Wednesday Dec. 12; Finals begin Dec. 15, 2018
Spring 2018 Seminars (Wednesdays at 2:00 in H425)
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  (in H705) "Singularities in  geometry, topology and strings"

Classes end Monday, April 30; Final Exams are May 4-9, 2018
Fall 2017 Seminars (Wednesdays at 2:00 in H525)
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, 2017

Spring 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


Here is a link to the algebra seminars in previous semesters

## Abstracts of seminar talks

### Fall 2018

In this talk, we present some properties of this convolution operation, as well as a recent result which states that after finitely many self convolutions every dominant morphism $f:X\to G$ from a smooth, absolutely irreducible variety X to an algebraic group G becomes flat with reduced fibers of rational singularities (this property is abbreviated FRS). The FRS property is of particular interest since by works of Aizenbud and Avni, FRS morphisms are characterized by having fibers whose point count over the finite rings $Z/p^kZ$ is well-behaved. This leads to applications in probability, group theory, representation growth and more. We will discuss some of these applications, and if time permits, the main ideas of the proof which utilize model-theoretic methods. Joint work with Itay Glazer.

Palindromicity and the local invariant cycle theorem (Patick Brosnan, December 12, 2018):
In its most basic form, the local invariant cycle theorem of Beilinson, Bernstein and Deligne (BBD) gives a surjection from the cohomology of the special fiber of a proper morphism of smooth varieties to the monodromy invariants of the general fiber. This result, which is one of the last theorems stated in the book by BBD, is a relatively easy consequence of their famous decomposition theorem.
In joint work with Tim Chow on a combinatorial problem, we needed a simple condition ensuring that the above surjection is actually an isomorphism. Our theorem is that this happens if and only if the special fiber has palindromic cohomology. I will explain the proof of this theorem and a generalization proved using the (now known) Kashiwara conjecture. I will also say a little bit about the combinatorial problem (the Shareshian-Wachs conjecture on Hessenberg varieties) which motivated our work.

### Fall 2017

#### 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.

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.

#### Spring 2016

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.

Charles Weibel / weibel @ math.rutgers.edu / January 1, 2018