Tuesday, October 5, 2021
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All day |
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4:00pm |
10/05/2021 - 4:15pm For a finite-type surface S, we study a preferred basis for the commutative algebra C[R_SL3(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora-Westbury. These basis elements come from the trace functions associated to certain tri-valent graphs embedded in the surface S. We show that this basis can be naturally indexed by positive integer coordinates, defined by Knutson-Tao rhombus inequalities and modulo 3 congruence conditions. These coordinates are related, by the geometric theory of Fock-Goncharov, to the tropical points at infinity of the dual version of the character variety. This is joint work with Zhe Sun. Location:
LOM 214
10/05/2021 - 4:30pm Deligne--Lusztig varieties are subvarieties of flag varieties whose cohomology encodes the representations of reductive groups over finite fields. These give rise to so-called "depth-zero" supercuspidal representations of p-adic groups. In this talk, we discuss geometric constructions of positive depth supercuspidal representations and the implications of such realizations towards the Langlands program. This is based on joint work with A. Ivanov and on joint work with M. Oi. Location:
Zoom
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