Last Update: July 20, 2007
Speaker: Matt Davis, University of Wisconsin
Title: Representations of Affine Hecke algebras
Abstract: TBA
Speaker: Martha Yip, University of Wisconsin
Title: Parking functions, Shi arrangements and representations
Abstract: TBA
Speaker: Zajj Daugherty, University of Wisconsin
Title: Graded diagram algebras
Abstract: The graded Birman-Murakami-Wenzl algebra arises as a tensor power centralizer algebra, an algebra of operators which preserve symmetries in a tensor space. The classical case, studied by Frobenius and Schur around 1900, provided the link between the representation theory of the symmetric group and the general linear group. In this talk, I will utilize combinatorial tools to explore the link between the actions of the graded BMW algebra and the symplectic and orthogonal Lie algebras on the tensor space.
Speaker: Zhaohu Nie, University of Texas A&M
Title: Cohomology theories for algebraic varieties
Abstract: I will discuss two topics: Hodge theory and motivic cohomology. For Hodge theory, I will start with the approach to the Hodge conjecture using singular hypersurfaces. Then I will discuss the related notions of singularities of a Hodge class and singularities of an admissible normal function, and the equivalence of the Hodge conjecture to the existence of such singularities. This part is joint work with P. Brosnan, H. Fang and G. Pearlstein. For motivic cohomology, I will present, after some background materials, a construction of the motivic reduced power operations following a topological analogue of Karoubi. If time permits (unlikely), I will briefly mention some other theories in this huge field.
Speaker: Julia Pevtsova, University of Washington
Title: Spectra of triangulated categories
Abstract: I shall start by discussing a general framework of studying tensor triangulated categories via geometric ideas as introduced by P. Balmer and then concentrate on two specific applications: to the category of modular representations of a finite group scheme and to the bounded derived category of a quotient stack.
Speaker: Rajesh Kulkarni, Michigan State University
Title: Self-dual sheaves on certain unitary Shimura varieties
Abstract:
Speaker: Nora Ganter, Colby College
Title: Representation theory and character theory in 2-categories
Abstract: In the 90, Hopkins, Kuhn and Ravenel studied general cohomology theories of classifying spaces of finite groups. In this context, they came across a character theory much like that of the representations of finite groups. The generalized group characters that turn up in this context are called 2-class functions; they are functions on pairs of commuting elements that are invariant under simultaneous conjugation
χ(g,h) = χ(s-1gs, s-1hs).
There are notions of transfer and restriction, inner products and the like. I will explain how a categorical notion of representation gives rise to a Hopkins-Kuhn-Ravenel type character theory. Time permitting, I will give a short overview over the appearance of generalized characters in various branches of mathematics.
Speaker: Alex Ghitza, Colby College
Title: Lifting automorphic forms from positive characteristic
Abstract: Modular forms (mod p) can be defined in two ways: (a) by reduction modulo p of modular forms over the integers, or (b) intrinsically, using the moduli space of elliptic curves over finite fields. The obvious question is whether the two definitions agree, and this was answered by Katz (yes, if the forms have weight 2 or higher) and by Mestre (no, for forms of weight 1). I will review these "classical" results and discuss the issues involved in extending them to other classes of automorphic forms, with emphasis on Siegel modular forms. The talk will be such that a lack of background knowledge can be made up for by having sufficient credulity in what I will claim.
Speaker: Arun Ram, University of Wisconsin
Title: Boundary diagram algebras
Abstract: This talk is about diagram algebras which come from the two-boundary braid group (braids with two poles). This is a generalization of recent work (from statistical mechanics) on two-boundary Temperley-Lieb algebras. The generalized setting naturally includes two boundary Hecke algebras and two-boundary BMW algebras. These algebras are like affine Hecke algebras (of type A) and affine BMW algebras except with two poles.
Speaker: Mathieu Willems, University of Ottawa
Title: A Chevalley formula in equivariant K-theory
Abstract: In this talk, I will give a Chevalley formula in equivariant K-theory. First, I will decompose the class of a line bundle in the equivariant K-theory of a Bott-Samelson variety. Then I will use this result to give a formula to multiply the class of a line bundle by the class of a Schubert variety in the equivariant K-theory of a flag variety.
Speaker: Henning Andersen, University of Aarhus
Title: Sum formulas in the representation theory of algebraic and quantum groups
Abstract: Let V be a Weyl module for a semisimple algebraic group G and let T be a tilting module. Important information about the composition factors of V and about the indecomposable summands of T is contained in the Jantzen filtrations of V and of HomG(V, T). We shall discuss joint work with U. Kulkarni in which give a unified proof of sum formulas for such filtrations. Our method also applies to the corresponding problem for quantum groups.
Speaker: Noah Kieserman, University of Wisconsin
Title: Integration and exponentiation
Abstract:
Speaker: Arun Ram, University of Wisconsin
Title: Centers of tantalizers
Abstract: Many diagram algebras arise as tantalizers. The Schur-Weyl duality makes it possible to steal most of the center of the tantalizer from the corresponding dual object in the duality. I will outline this process and explain how combinatorial results pop out of the picture. This talk is based on joint work with Zajj Daugherty and Rahbar Virk.
Speaker: Nathan Geer, Georgia Tech
Title: An invariant trace for the category of representations of Lie superalgebras
Abstract: In this talk I will discuss a renormalization of the supertrace on the category of representations of Lie superalgebras, by a kind of "fake superdimension." The genuine superdimensions and supertraces are generically zero. However, the "fake superdimensions" are non-zero and lead to a kind of supertrace which is non-trivial and invariant. The proof I will discuss uses quantum algebra and low-dimensional topology but surprisingly the statements about representations of Lie superalgebras are completely classical statements. This is joint work with Bertrand Patureau-Mirand.
Speaker: Helene Barcelo, Arizona State University
Title: The Discrete Fundamental Group of the Order Complex of Bn.
Abstract: We prove combinatorially that the first Betti number of the complement of the $3$-equal arrangement is equal to $2^{n-3}(n^2-5n+8)-1.$ This formula was originally obtained by Bj\"orner and Welker in 1995. We use a notion of discrete homotopy to reformulate the problem into one of counting certain equivalence classes of $6$-cycles in the graph corresponding to the $1$-skeleton of the permutahedron. We then use the language of words, over the alphabet of simple transpositions, to obtain necessary and sufficient conditions to determine if two $6$-cycles belong to the same class. The proof requires only simple combinatorial arguments.
Speaker: Matt Davis, University of Wisconsin, Madison
Title: On indexing affine Hecke algebra representations
Speaker: John Bowman, University of Wisconsin
Title: Finite dimensional modules for affine quantum groups
Speaker: Rahbar Virk, University of Wisconsin, Madison
Title: On centers
Speaker: Zajj Daugherty, University of Wisconsin, Madison
Title: Introduction to affine and graded BMW algebras
Speaker: Lauren Williams, Harvard University
Title: From total positivity on the Grassmanian to the asymmetric exclusion process
Speaker: Martha Yip, University of Wisconsin, Madison
Title: Counting noncrossing partitions and regions
Speaker: Arun Ram, University of Wisconsin, Madison
Title: Introduction to moment maps on flag varieties
Speaker: Stefko Miklavic, University of Ljubljana
Title: sl_2 actions on graphs
Speaker: Petra Hitzelberger, University of Muenster
Title: What is a Λ-building?
Abstract: We will discuss the definition of affine Λ-buildings, which are generalisations of simplicial affine buildings, give some of their properties and an example.
Speaker: Fred Goodman, University of Iowa
Title: Something about BMW algebras?
Speaker: Seok-Jin Kang, Seoul National University
Title: Abstract crystals for generalized Kac-Moody algebras