"Vertex algebras associated with elliptic affine Lie algebras"
Time: 11:45 AM
Location: Hill 425
Abstract:
Elliptic affine Lie algebras, similar to the usual affine Lie
algebras, are a family of infinite-dimensional Lie algebras associated
to finite-dimensional simple Lie algebras. It has been long known that
affine Lie algebras have a canonical association with vertex algebras
and their modules. In this talk, we will show how to associate
elliptic affine Lie algebras with what are called vertex
$C((z))$-algebras and their modules in a certain category.
Friday, November 13th
Zhenghan Wang , Microsoft and University of California at Santa Barbara (PLEASE NOTE TIME CHANGE!)
"CFT, MTC, and FQH states"
Time: 11:55 AM
Location: Hill 425
Abstract: We will discuss the CFT approach to groundstate wavefunctions of electrons in fractional quantum Hall (FQH) liquids initiated by G. Moore and N. Read in 1991. In this approach, groundstates of an electron liquid are given by conformal blocks of a rational CFT, and the topological properties of the quasi-particles are described by the associated modular tensor category. Open problems include the Moore-Read Holo=Mono conjecture, and classifications of FQH states.
Friday, November 6th
Dmitry Gourevitch, Institute for Advanced Study
"Smooth Transfer of Kloosterman Integrals (the Archimedean case)"
Time: 11:45 AM
Location: Hill 425
Abstract: We establish the existence of a transfer, which is compatible with Kloosterman integrals, between Schwartz functions on GL(n,R) and Schwartz functions on the variety of non-degenerate Hermitian forms. Namely, we consider an integral of a Schwartz function on GL(n,R) along the orbits of the two sided action of the groups of upper and lower unipotent matrices twisted by a non-degenerate character. This gives a smooth function on the torus. We prove that the space of all functions obtained in such a way coincides with the space that is constructed analogously when GL(n,R) is replaced with the variety of non-degenerate hermitian forms. We also obtain similar results for gl(n,R). This theorem is important in the relative trace formula.
The non-Archimedean case is done by Jacquet in 2003 and our proof follows the same lines. However we had to face serious additional difficulties that appear only in the Archimedean case.
Friday, October 30th
Georgia Benkart, University of Wisconsin at Madison
" Quantum sl(2) and Temperley-Lieb-type Combinatorics"
Time: 11:45 AM
Location: Hill 425
Abstract: This talk will feature various algebras of diagrams (some old,
some new) that have beautiful algebraic and combinatorial
properties and are related to the representation theory
of quantum sl(2).
Friday, October 23rd
Nigel Boston, University of Wisconsin
" Random Groups and Random Galois Groups"
Time: 11:45 AM
Location: Hill 425
Abstract: In analogy to work of Dunfield and Thurston in topology, we computed the probability that a random pro-p presentation will yield a given p-group G. Now in joint work with Jordan Ellenberg we give a heuristic for the probability that the maximal pro-p extension of Q unramified outside a random set of primes will have Galois group G. This is guided by the Cohen-Lenstra heuristics and the theory of pro-p braid groups.
Friday, October 16th
Alex Feigold, Binghamton University, State University of New York
"A New Perspective on the Frenkel-Zhu Fusion Rule Theorem"
Time: 11:45 AM
Location: Hill 425
Abstract: Fusion rules are analogous to tensor product multiplicities, and play an important role in conformal field theory. They are dimensions of spaces of intertwining operators determined by a triple of irreducible modules for a vertex operator algebra. An important class of examples, known in physics as Wess-Zumino-Witten models, comes from the theory of affine Kac-Moody Lie algebras, where the modules are the standard modules of a fixed non-negative integral level. This talk is an exposition of joint work with Stefan Fredenhagen (2008) in which we prove a formula for fusion coefficients of affine Kac-Moody algebras first conjectured by Walton (1994). It is a reformulation of the Frenkel-Zhu affine fusion rule theorem (1992), written so that it can be seen as a beautiful generalization of the classical Parasarathy-Ranga Rao-Varadarajan tensor product theorem (1967).
Friday, October 9th
Vladimir Retakh, Rutgers University
"Towards noncommutative cluster algebras"
Time: 11:45 AM
Location: Hill 425
Abstract: Commutative cluster algebras were introduced by Fomin and Zelevinsky in 2002. they appeared to be very useful in many areas of representations theory. In my talk I will discuss a number of examples that could lead to a theory of noncommutative cluster algebras.
Friday, October 2nd
Lev Borisov, Rutgers University
"In search of families of dg-algebras related to resolutions of Gorenstein toric singularities"
Time: 11:45 AM
Location: Hill 425
Abstract: A Gorenstein toric singularity can be described by simple combinatorial data, namely a convex polytope $P$ in ${bf Z}^n$ with integer vertices. Different triangulations of $P$ with vertices given by integer points of $P$ give rise to different resolutions of the singularity. It has been shown that bounded derived categories of coherent sheaves on these resolutions are equivalent. It is reasonable to expect that there is in fact a continuous family of triangulated categories that includes these categories as its limit points. This is very much work in progress, and the main questions are still wide open. It is my hope that by bringing this problem to your attention I can inspire someone to find such construction.
Friday, September 18th
Christopher Sadowski, Rutgers University, Christopher Sadowski, Rutgers University
"On a symmetry of the category of integrable modules (joint work with Bill Cook)"
Time: 11:45 AM
Location: Hill 423
Abstract: Haisheng Li showed that given a module (W, Y_W(cdot, x))
for a vertex algebra (V, Y (cdot, x)), one can obtain a new V-module
W^{Delta}= (W, Y_W(Delta(x)cdot, x)) if Delta(x) satisfies
certain natural conditions. Li presented a collection of such
Delta-operators for V=L(k, 0) (a vertex operator algebra associated
with an affine Lie algebra, k a positive integer). In this paper,
for each irreducible L(k, 0)-module W, we find a highest weight
vector of W^{Delta} when Delta is associated with a minuscule
coweight. From this we completely determine the action of
these Delta-operators on the set of isomorphism equivalence classes of
L(k, 0)-modules.
Friday, September 11th
Birne Binegar, Oklahoma State University
" W-Cells, Nilpotent Orbits, Primitive Ideals and Weyl Group Representations"
Time: 11:45 AM
Location: Hill 423
Abstract: Let $G$ be the real points of a connected linear reductive
complex algebraic group defined over $mathbb{R}$ and let $widehat
{G}_{adm,lambda}$ be the set of equivalences classes of irreducible
admissible representations of $G$ of infinitesimal character $lambda$,
which we assume to be regular and integral. The Atlas software enumerates
the
representations in $widehat{G}_{adm,lambda}$, and computes the
Kazhdan-Lusztig-Vogan polynomials $P_{x,y}left( qright) $ which not only
prescribe the Jordan-H"older decomposition of standard modules in terms
of the irreducibles in $widehat{G}_{lambda,adm}$, the KLV polnomials can
also be used to endow the set $widehat{G}_{adm,lambda}$ with the structure
of a $W$-graph, a certain weighted directed graph. The strongly connected
components of this $W$-graph are W-cells. In this talk I will describe how
the weighted graph structure of an W-cell $mathcal{C}$ allows one to
compute
the (common) associated variety of the annihilators of the representations
in
$mathcal{C}$ and, moreover, allows one to determine exactly when two
representations $x,yinmathcal{C}$ share the same annihilator.
This page was last updated on September 16, 2009 at 12:37 pm and is maintained by webmaster@math.rutgers.edu.
