Speaker: Qing Zhang

In this talk, we will discuss two integrals involving the exceptional group G2, both discovered by D. Ginzburg. The first integral gives an integral representation of the adjoint L-function of GL(3). Then I will report my recent work joint with J. Hundley on the holomorphy of adjoint L-function of GL(3). The second integral gives an integral representation of standard L-function of G2 itself. Related to this integral, we can consider a Fourier-Jacobi model for G2. I will discuss recent work joint with B. Liu on the uniqueness of such models over finite fields.

http://www.birs.ca/events/2018/focussed-research-groups/18frg237

Speaker: Reggie Lybbert

In their 1997 paper, _Geometric construction of crystal bases_ (Duke Math Journal, Vol 89, No. 1), Masaki Kashiwara and Yoshihisa Kashiwa Saito described a singularity in a quiver representation variety of type A_5 with the property that the characteristic cycles of the singularity is reducible, this providing a counterexample to a conjecture of Kazhdan and Lusztig. This singularity is now commonly know at the Kashiwara-Saito singularity. While the 1997 paper showed that the characteristic cycles of the Kashiwara-Saito singularity decomposes into at least two irreducible cycles, they promised, but did not prove, that it decomposes into exactly two irreducible cycles. Using techniques developed in the example part of the Voganish paper, augmented by some computational tools developed this summer, we believe we have a proof of this promise. In this seminar we'll give a sketch of the proof.

Using this calculation and the local Langlands correspondence for GL(16), we should be able to exhibit an irreducible representation \pi of p-adic GL(16) with the property that its ABV-packet (as defined in the Voganish paper) contains exactly one other irreducible representation, \pi', and also describe that representation. We refer to this \pi as the Kashiwara-Saito representation of GL(16) and to \pi' as its coronal representation. This will provide the smallest known example of an irreducible representation of p-adic general linear group with one coronal representation.

Locations: Zoom (https://zoom.us/j/238450154), Calgary, Lethbridge

Locations: Zoom, Calgary, Paris, Lethbridge

Andrew, Bin and Clifton
Zoom, Lethbridge, Beijing and Calgary

Speaker: Andrew Fiori

Location: Zoom, Paris, Calgary and Lethbridge

Topic: Progress on the Fourier transform and induction for Vogan varieties!
Details in our github repo.

Speaker: Andrew Fiori

Location: Zoom, Beijing, Calgary and Lethbridge

Topic: How to enumerate all stata in Vogan varieties for GL(n). Quivers perspective.
Some observations about the Kashiwara-Saito singularity in the Vogan variety for GL(16).

Speaker: Reginald Lybbert

Location: Calgary, MS337