Representation Theory and Number Theory Seminar, 2018-2019

Fall 2018: Friday, 3:30-4:30 PM, LCB 215



August 24:
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Title: Organizational meeting, 4:10-4:30
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August 31:
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September 7:
Speaker: Tony Feng, Stanford University
Title: The Artin-Tate pairing on the Brauer group of a surface
Abstract: There is a canonical pairing on the Brauer group of a surface over a finite field, and an old conjecture of Tate's predicts that this pairing is alternating. In this talk I will present a resolution to Tate’s conjecture. The key new ingredient is a circle of ideas originating in algebraic topology, centered around the Steenrod operations. The talk will advertise these new tools (while assuming minimal background in algebraic topology).

September 14:
Speaker: Adam Brown, The University of utah
Title: Arakawa-Suzuki functors for Whittaker modules
Abstract: The category of Whittaker modules, as formulated by Milicic and Soergel, is a category of Lie algebra representations which generalizes other well-studied categories of representations, such as the Bernstein-Gelfand-Gelfand category O. In this talk we will construct a family of exact functors from the category of Whittaker modules to the category of finite-dimensional graded affine Hecke algebra modules, for type A_n. These algebraically defined functors provide us with a representation theoretic analogue of certain geometric relationships, observed independently by Zelevinsky and Lusztig, between the flag variety and the variety of graded nilpotent classes. Using this geometric perspective and the corresponding Kazhdan-Lusztig conjectures for each category, we will prove that these functors map simple modules to simple modules (or zero). Moreover, we will see that each simple module for the graded affine Hecke algebra can be realized as the image of a simple Whittaker module.

September 21:
Speaker: Gil Moss, The University of Utah
Title: Characterizing the mod-\ell local Langlands correspondence for GL(n) using nilpotent gamma factors.
Abstract: In the complex representation theory of GL_n of a p-adic field, Rankin-Selberg gamma factors uniquely determine the supercuspidal support of a generic representation. This is known as a "converse theorem." By using a modified gamma factor that accounts for nilpotent elements in the mod-\ell Bernstein center, we can establish a converse theorem in the mod-\ell setting, addressing a conjecture of Vigneras. With an appropriate modification of gamma factors on the Galois side, this would give a characterization of Vigneras' mod-\ell local Langlands correspondence.

September 28:
Speaker: Kei Yuen Chan, University of Georgia
Title: Ext-branching law for reductive p-adic groups
Abstract: The local Gan-Gross-Prasad conjecture predicts the branching law for some tempered representations of classical reductive groups over real and p-adic fields. Dipendra Prasad suggests homological variations of those branching problems and in particular conjectures that there is no higher extensions between a generic representation of GL(n+1,F) and a generic one of GL(n,F). In a joint work with Gordan Savin, we give a positive answer to the conjecture. I shall report the work and other relevant results in the talk.

October 5:
Speaker: Stefan Patrikis, The University of Utah
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October 12: No Seminar (fall break)
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October 19:
Speaker: Sabine Lang, The University of Utah
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October 26:
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November 2:
Speaker: Christian Klevdal, The University of Utah
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November 9:
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November 16:
Speaker: Claus Sorensen, University of California, San Diego
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November 23: No Seminar (Thanksgiving break)
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November 30:
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December 7:
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