Department of Mathematics - Lie Groups and Rep Theory Seminar

Starting fall of 2021 the seminar will be hybrid. When possible it will be held in person in the Colloquium Room (3206) of the mathematics department. In additition it will be available live on Zoom. The password is the first six Fibonacci numbers (starting at 0). University of Maryland users will be admitted directly. Other users should use their first and last names, and will be admitted from the waiting room. In many cases the video and/or slides will be available on this page following the lecture.

Algebra Number Theory Seminar

Videos and Slides fall 2021 to spring 2022:

Jeffrey Adams, September 22: Arthur and ABV packets
Jeffrey Adams, September 29: Arthur and ABV packets II

Videos and Slides fall 2020 to spring 2021:

Robert Cass, September 14: A mod p geometric Satake isomorphisms
Sam Mundy, September 30: An Arthur packet for real splilt G₂
Dan Ciubotaru, October 5: An elliptic Fourier transform for unipotent representations of p-adic groups - (Note: the recording starts a few seconds late. The top lines of the slide say: Gamma is a finite group, (V,delta) is a representation, and v is in V)
Igor Rapinchuk, October 21: Algebraic groups with good reduction
Laura Rider, October 26: Modular perverse sheaves on the affine flag variety
XuhuaHe, November 11: Affine Deligne-Luztig varieties and generalized affine Springer fibers (slides)
Eugen Hellmann 1, November 16: On the Derived Category of the Iwahori-Hecke algebra 1 (slides)
Eugen Hellmann 2, November 18: On the Derived Category of the Iwahori-Hecke algebra 2 (slides)
Jessica Fintzen, November 23: Representations of p-adic groups (slides)
Jessica Fintzen , November 30: From representations of p-adic groups to congruences of automorphic forms
Lucas Mason-Brown, December 14: What is a unipotent representation? (slides)
Pol van Hoften, February 8, Mod p points on Shimura varieties of parahoric level I
Pol van Hoften, February 10: Mod p points on Shimura varieties of parahoric level II
Wee Teck Gan, April 5: Howe to transfer Harish Chandra characters via Weil's representation (slides)
Meinolf Geck, April 7: On the Computation of Green Functions (slides)

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Abstract: Let G be a connected reductive group defined over a finite or a non-archimedean local field F. We show that G(F) admits cuspidal representations when F is finite and supercuspidal representations when F is non-archimedean local. We also determine precisely when G(F) admits self-dual representations. For the results on self-duality, we assume some hypothesis on G. These hypotheses disallow G to have certain small rank factors when the field (in case F is finite) or the residue field (in case F is non-archimedean local) is of cardinality ≤ 5. When F is non-archimedean local and G is ramified, these hypotheses impose some additional restrictions on G. This is a joint work with Jeff Adler.

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Abstract: In 1983 Jim Arthur conjectured the existence of certain sets of representations
of a reductive group G over a local field F, associated to homomorphisms from the Weil-Deligne group x SL(2) into the L-group of G. In the case of split classical groups he defined these "Arthur" packets in his 2010 book. For F=R Adams, Barbasch and Vogan gave a definition in their 1992 book, commonly referred to as ABV. Nicolas Arancibia and Paul Mezo, with some help from the speaker, have proved these two definitions agree when they are both defined.

The talk will be available online at https://umd.zoom.us/j/96890967721

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Abstract: Let G be a special parahoric group scheme of twisted type, excluding the absolutely special case for ramified odd unitary group. Using the methods and results of Zhu, we prove a duality theorem for G: there is a duality between the level one twisted affine Demazure modules and the function rings of certain torus fixed point subschemes in the affine Schubert varieties of G. Along the way, we also establish the duality theorem for untwisted E_6. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of G. In particular, this confirms a conjecture of Haines and Richarz. This talk is based on the joint work with Marc Besson.

Lie Groups and Representation Theory Seminar

Speaker: Manish Mishra (IISER Pune) - https://sites.google.com/site/manishmishra/

View Abstract

Speaker: Jeffrey Adams (University of Maryland) -

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Speaker: Jeffrey Adams (University of Maryland) -

Speaker: Jiuzu Hong (UNC) - https://hong.web.unc.edu/

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Speaker: Jonathan Wang (Perimeter Institute) -

Speaker: Jonathan Wang (Perimeter Insititue) -