Fall, 2011

Fall, 2011

  • Speaker Abid Ali, Rutgers University
    • Title Congruence subgroups of lattices in rank 2 Kac-Moody groups over finite fields
    • Time/place 9/30/2011, Friday, 11:45 am in Hill 705
    • Abstract In this talk, I will present joint work with Prof. Lisa Carbone. We define congruence subgroups K_{U^-}, K_{B^-} and K_{P^-_1} of U^-, B^- and P^-_1 as natural generalizations of the corresponding notions for lattices in Lie groups. It is known that the groups U^-, B^- and P^-_1 are non-uniform lattice subgroups of G. When G is a complete rank 2 Kac-Moody group over a finite field, G is locally compact and totally disconnected. The subgroup B^- = HU^- where H is a `diagonal subgroup' and U^- is generated by all negative real root groups, P^-_1 = B^- \cup B^- w_1 B^- is the standard parabolic subgroup of the negative BN-pair for G. Our technique involves determining graphs of groups presentations for U^-, B^- and P^-_1. We explicitly construct the graphs of groups for congruence subgroups K_{U^-}, K_{B^-} and K_{P^-_1} of U^-, B^- and P^-_1 respectively.

  • Speaker Dan Barbasch, Cornell University
    • Title Unipotent representations for Sp(p,q) and O*(n)
    • Time/place 10/14/2011, Friday, 11:45 am in Hill 705
    • Abstract In this work, joint with P. Trapa, we establish the unitarity of the unipotent representations in the sense of Arthur or Adams-Barbasch-Vogan for the real forms Sp(p,q) and O*(n). Unipotent representations are conjectured to be the building blocks of the unitary fual of a reductive real group. The techniques rely heavily on properties of the associated cycle or asymptotic support of an admissible module.

  • Speaker Jerry Goldin, Rutgers University
    • Title Diffeomorphism Group Representations and Anyonic Statistics
    • Time/place 10/21/2011, Friday, 11:45 am in Hill 705
    • Abstract I shall first review how a fundamental approach to quantum mechanics based on unitary representations of diffeomorphism groups led to an early prediction of anyonic statistics in (2+1)-dimensions, including nonabelian anyons obtained by inducing from higher-dimensional braid group representations. Then I shall point to some analogous possibilities for infinite-dimensional configuration spaces, including anyonic statistics for extended objects in 3-dimensional space.

  • Speaker Antun Milas, State University of New York at Albany
    • Title Some irregular representations of vertex algebras
    • Time/place 10/28/2011, Friday, 11:45 am in Hill 705
    • Abstract I'll be discussing constructions and properties of certain "irregular" representations of non-rational vertex algebras. The main motivation for this line of work comes from the AGT conjecture in physics, relating 2d CFTs and certain 4d supersymmetric field theories. This talk is meant to be accessible to graduate students interested in Lie theory.

  • Speaker Daniele Rosso, University of Chicago
    • Title Classic and mirabolic RSK correspondence for partial flags
    • Time/place 11/11/2011, Friday, 11:45 am in Hill 705
    • Abstract The Robinson-Schensted-Knuth correspondence is a purely combinatorial statement, but Steinberg and Spaltenstein independently found that it relates the relative position of two complete flags to the irreducible components of the flag variety in which they lie. Travkin then gave an algorithm for the case of 'mirabolic' varieties of complete flags. We will see how to generalize both results to the case of partial flags.

  • Speaker Vladimir Retakh, Rutgers University
    • Title A short proof of Kontsevich cluster conjecture
    • Time/place 11/18/2011, Friday, 11:45 am in Hill 552 (the colloquium room of the statistics department; note that the room is changed from Hill 705 to Hill 552 on that day)
    • Abstract We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by noncommutative Laurent polynomials. (Joint work with Arkady Berenstein)

  • Speaker Haisheng Li, Rutgers University at Camden
    • Title On certain notions of quantum vertex (operator) algebra
    • Time/place 12/02/2011, Friday, 11:45 am in Hill 705
    • Abstract In the literature, there have been several notions of quantum vertex (operator) algebra. The very first, called deformed chiral algebra, was introduced by E. Frenkel and N. Reshetikhin, while the second, called quantum vertex operator algebra, was introduced by P. Etingof and D. Kazhdan. Later, essentially following Etingof-Kazhdan, we introduced a notion of quantum vertex algebra. In this talk, I will discuss a connection between this particular theory of quantum vertex algebras and the Frenkel-Reshetikhin theory. For this talk, I shall sketch the basic definitions and no pre-knowledge on quantum vertex algebras is assumed. I will emphasize the conceptual aspect, minimizing the technical part.

  • Speaker Corina Calinescu, Yale University
    • Title Vertex-algebraic structure of representations of affine Lie algebras
    • Time/place 12/09/2011, Friday, 11:45 am in Hill 705
    • Abstract This talk is an overview of the known results and open problems about the principal subspaces of standard modules for certain untwisted and twisted affine Lie algebras. We discuss vertex-algebraic structure of principal subspaces and their fermionic characters. This is joint work with Jim Lepowsky and Antun Milas. The talk will be introductory.