Representation Theory Seminar

Representation Theory Seminar
2012-2013
Fridays 2:00-3:00 in LCB 215

2011-2012: 2011-2012
2010-2011: 2009-2010
2009-2010: 2009-2010

Date	Speaker	Title
September 7	Hung Yean Loke (National University of Singapore)	Exceptional Lie algebras over the rational field and Tits' construction
September 14	Aaron Wood (University of Utah)	A minimal type of the 2-adic Weil representation
September 21	Aaron Wood (University of Utah)	A minimal type of the 2-adic Weil representation
September 28	Mark Reeder (Boston College)	Formal degrees and the Langlands correspondence
October 5	Dani Szpruch (Purdue University)	TBA
November 16	Colleen Robles (Texas A&M University)	The role of representations in Hodge theory
November 30	Dan Ciubotaru (University of Utah)	Green polynomials and spin representations of Weyl groups
February 8	Moshe Adrian (University of Utah)	Hecke algebras and simple supercuspidal representations
February 15	Gordan Savin (University of Utah)	A tale of two Hecke algebras
February 22	Gordan Savin (University of Utah)	Matching of Hecke algebras in exceptional theta correspondences
March 8	Loren Spice (Texas Christian University)	Stability and sign changes in p-adic harmonic analysis
March 22	Colleen Robles (Texas A&M University)	Characteristic cohomology associated to variation of Hodge structure
March 29	Monty McGovern (University of Washington)	Rational singularity of nilpotent varieties
April 5	Moshe Adrian (University of Utah)	Rectifiers and the local Langlands correspondence

September 7, 2012
Hung Yean Loke
Title: Exceptional Lie algebras over the rational field and Tits' construction
Abstract: In this talk, I show that Tits' construction gives all the Lie algebras defined over the rational field which are of type F4, E6, E7, and E8. In particular, each exceptional Lie algebra contains a dual pair h_1+h_2 defined over the rational field where h_1 is of type G2 and H_2 is of type A1, A2, C3, and F4, respectively. Finally, I will show that the rational dual pair uniquely determines the rational form of the exceptional Lie algebra. This is a joint project with Gordan Savin.

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September 14 and 21, 2012
Aaron Wood
Title: A minimal type of the 2-adic Weil representation
Abstract: Recently, Gan and Savin have used minimal types of the Weil representation to describe correspondences of Hecke algebras between some representations of metaplectic groups and some representations of orthogonal groups. In the case of odd residual characteristic, these were types of the Iwahori subgroup. However, the 2-adic Weil representation has no Iwahori-fixed vectors. In these talks, I will discuss a minimal type for p=2 and describe the corresponding Hecke algebra. In the end, this Hecke algebra will be shown to be isomorphic to the classical affine Hecke algebra of type B_n.

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September 28, 2012
Mark Reeder
Title: Formal degrees and the Langlands correspondence
Abstract: I will discuss examples showing how formal degrees provide, or fail to provide, uniqueness in the local Langlands correspondence.

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October 5, 2012
Dani Szpruch
Title: TBA
Abstract:

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November 16, 2012
Colleen Robles
Title: The role of representations in Hodge theory
Abstract: I will describe the role of Lie theory in the study of Hodge structures. This will include: (i) the notions of Hodge group and Hodge representation, recently introduced by Green--Griffiths--Kerr; and (ii) some questions, of a representation theoretic nature, that arise in Hodge theory.

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November 30, 2012
Dan Ciubotaru
Title: Green polynomials and spin representations of Weyl groups
Abstract: In joint work with Xuhua He, we give a reformulation of the algorithm of Lusztig and Shoji for computing the graded representation of the Weyl group W on the cohomology of Springer fibers. As an application, we obtain a new description of the representations of the pin double cover of W.

February 8, 2013
Moshe Adrian
Title: Hecke algebras and simple supercuspidal representations
Abstract: TBA

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February 15, 2013
Gordan Savin
Title: A tale of two Hecke algebras
Abstract:   TBA

February 22, 2013
Gordan Savin
Title: Matching of Hecke algebras in exceptional theta correspondences
Abstract:   TBA

March 8, 2013
Loren Spice
Title: Stability and sign changes in p-adic harmonic analysis
Abstract:   Reeder has described a conjectural candidate for the partition of certain supercuspidal representations constructed by Yu (the so called toral, unramified supercuspidals) into L-packets, and verified that it satisfies most of the necessary properties. However, the problem of stability of the appropriate character sums remained outstanding. In this talk, I will discuss joint work with DeBacker that shows the necessary stability. A key ingredient is the study of a sign associated to combinatorial data involving Galois orbits on a root system, which we can compute unconditionally in the unramified case.

March 22, 2013
Colleen Robles
Title: Characteristic cohomology associated to variation of Hodge structure
Abstract:   TBA

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March 29, 2013
Monty McGovern
Title: Rational singularity of nilpotent varieties
Abstract: I will present two methods for computing the rational singular locus of a nilpotent variety (closure of a nilpotent orbit) in a complex semisimple Lie algebra, one of them using a torus action and singular cohomology, the other intersection cohomology. Both methods actually compute the dimension of the cohomology of the variety at each point. I will also give an example of a nilpotent variety whose rational singular locus has codimension 2; this phenomenon cannot occur for Schubert varieties.

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April 5, 2013
Moshe Adrian
Title: Rectifiers and the local Langlands correspondence
Abstract: In this talk, I will recall the notion of a rectifier as in the work of Bushnell/Henniart in the local Langlands correpsondence for GL(n). I will then propose a definition for rectifier for general groups G. I will then describe rectifiers in the so called tame setting, and show that our definition agrees with Bushnell/Henniart's in this setting. This is joint work with David Roe.

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