Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020

• A mod p geometric Satake isomorphism

  Speaker: Robert Cass (Harvard) - http://people.math.harvard.edu/~rcass/
  

  When: Mon, September 14, 2020 - 2:00pm
  Where: Zoom
  

  View Abstract

  View Abstract

  Abstract: We explain a mod p version of the geometric Satake isomorphism which gives a sheaf-theoretic description of the spherical mod p Hecke algebra. In our setup the mod p Satake category is not controlled by the dual group but rather a certain affine monoid scheme. Our proofs rely crucially on the theory of F-singularities, and along the way we prove new results about the singularities of affine Schubert varieties. We also discuss some further results on the resulting monoid in joint work with Cedric Pepin.
  
• An Arthur packet for real split G_2

  Speaker: Sam Mundy (Columbia University) - Abstract: In this talk we will have fun manipulating Arthur parameters for the exceptional group G_2. We will use these parameters to construct certain Arthur packets for G_2 via the work of Adams--Johnson. This is motivated by trying to understand cohomological properties of CAP representations for G_2.
  

  When: Wed, September 30, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/96890967721
  

  View Abstract

  View Abstract

  Abstract: In this talk we will have fun manipulating Arthur parameters for the exceptional group G_2. We will use these parameters to construct certain Arthur packets for G_2 via the work of Adams--Johnson. This is motivated by trying to understand cohomological properties of CAP representations for G_2.
  
• An elliptic Fourier transform for unipotent representations of p-adic groups

  Speaker: Dan Ciubotaru (Oxford) - Abstract: An important ingredient in the character theory of finite groups of Lie type is Lusztig's nonabelian Fourier transform which is the change of basis matrix between the basis of irreducible characters and the basis of "almost characters" (trace functions for character sheaves). The expectation is that a similar picture should exist for admissible representations of reductive p-adic groups, and in the case of representations with unipotent cuspidal support, Lusztig (2014) proposed several conjectures. Independently, Moeglin and Waldspurger defined an involution on the space of tempered unipotent representations of the odd orthogonal groups as part of their proof of the stability of tempered unipotent L-packets. Motivated by a more recent reformulation of this involution by Waldspurger (2017), we define a "nonabelian Fourier transform" on the space of elliptic representations of a semisimple p-adic group and verify, for split exceptional groups, that it commutes, via maximal parahoric restrictions, with Lusztig's Fourier transform for the finite reductive quotients.
  

  When: Mon, October 5, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/96890967721
  

  View Abstract

  View Abstract

  Abstract: An important ingredient in the character theory of finite groups of Lie type is Lusztig's nonabelian Fourier transform which is the change of basis matrix between the basis of irreducible characters and the basis of "almost characters" (trace functions for character sheaves). The expectation is that a similar picture should exist for admissible representations of reductive p-adic groups, and in the case of representations with unipotent cuspidal support, Lusztig (2014) proposed several conjectures. Independently, Moeglin and Waldspurger defined an involution on the space of tempered unipotent representations of the odd orthogonal groups as part of their proof of the stability of tempered unipotent L-packets. Motivated by a more recent reformulation of this involution by Waldspurger (2017), we define a "nonabelian Fourier transform" on the space of elliptic representations of a semisimple p-adic group and verify, for split exceptional groups, that it commutes, via maximal parahoric restrictions, with Lusztig's Fourier transform for the finite reductive quotients.
  
• Algebraic groups with good reduction

  Speaker: Igor Rapinchuk (Michigan State University) - https://sites.google.com/site/irapinchuk1/home
  

  When: Wed, October 21, 2020 - 2:00pm
  Where: Zoom
  

  View Abstract

  View Abstract

  Abstract: Techniques involving reduction are very common in number theory and arithmetic geometry. In particular, elliptic curves and general abelian varieties having good reduction have been the subject of very intensive investigations over the years. The purpose of this talk is to report on recent work that focuses on good reduction in the context of reductive linear algebraic groups over finitely generated fields. In addition, we will highlight some applications to the study of local-global principles and the analysis of algebraic groups having the same maximal tori. (Parts of this work are joint with V. Chernousov and A. Rapinchuk.)
  
• TBA

  Speaker: Laura Rider (University of Georgia) - Modular Perverse Sheaves on the affine Flag Variety
  

  When: Mon, October 26, 2020 - 2:00pm
  Where: https://umd.zoom.us/j/96890967721
  

  View Abstract

  View Abstract

  Abstract: There are two categorical realizations of the affine Hecke algebra: constructible sheaves on the affine flag variety and coherent sheaves on the Langlands dual Steinberg variety. A fundamental problem in geometric representation theory is to relate these two categories by a category equivalence. This was achieved by Bezrukavnikov in characteristic 0 about a decade ago. In this talk, I will discuss a first step toward solving this problem in the modular case joint with R. Bezrukavnikov and S. Riche.
  
• TBA

  Speaker: Moshe Adrian (Queens College) -
  

  When: Mon, November 2, 2020 - 2:00pm
  Where: Online
  
• Affine Deligne-Lusztig varieties and Generalized affine Springer fibers

  Speaker: Xuhua He (CUHK) -
  

  When: Wed, November 11, 2020 - 8:00am
  Where: Online
  

  View Abstract

  View Abstract

  Abstract: The notion of affine Springer fiber was introduced by Kazhdan and Lusztig in 1988. It plays a crucial role in the geometric representation theory and the Langlands program. The generalized affine Springer fibers were first studied by Kottwitz and Viehmann for the hyperspecial level structure in 2012 and by Lusztig for arbitrary parahoric level structure in 2015. Many geometric properties for the hyperspecial level structure were further studied by Bouthier and Chi.
  
  In this talk, I will propose a new approach to study the generalized affine Springer fibers. The key observation is that the affine Deligne-Lusztig varieties, in some sense, may be regarded as the ``shadow'' of generalized affine Springer fibers. I will also explain some ingredients used to deduce some geometric properties (nonemptiness, dimension, irreducible components) of generalized affine Springer fibers from the properties of the affine Deligne-Lusztig varieties. This talk is based on a work in progress.
  
• TBA

  Speaker: Eugen Hellmann (U. Münster) -
  

  When: Mon, November 16, 2020 - 2:00pm
  Where: Online
  
• TBA

  Speaker: Eugen Hellmann (U. Münster) -
  

  When: Wed, November 18, 2020 - 2:00pm
  Where: Online
  
• TBA

  Speaker: Jessica Fintzen (Cambridge U./Duke U) -
  

  When: Mon, November 23, 2020 - 2:00pm
  Where: Online
  
• TBA

  Speaker: Jessica Fintzen (Cambridge U/Duke U) -
  

  When: Mon, November 30, 2020 - 2:00pm
  Where: Online
  
• TBA

  Speaker: Tasho Kaletha (U. Michigan) -
  

  When: Mon, December 7, 2020 - 2:00pm
  Where: Online