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

Overview of the Voganish Project

Statement of summer objectives: Microlocal vanishing cycles of the Kashiwara-Saito singularity

Divide and conquer:
Nicole Kitt: Calculations using the Fourier transform
Reginald Lybbert: Calculations using resolution of singularities

Location: University of Calgary, MS 337

The Fourier transform we're using is taken from Kashiwara and Shapira by way of Schurmann, and has the vanishing cycles functor built in. Today we're working on establishing and documenting the main properties of this functor.

Andrew and Clifton, at the University of Lethbridge

Speaker: Kam-Fai Tam (Max-Planck-Institut für Mathematik, Bonn)

Title: Construction of supercuspidal representations

Location: Hilbert Seminar Room (MS 337)

Time: Thursday, April 5, 14:00--15:00

Abstract: Given a supercuspidal representation of GL_2 over a p-adic field or the group U_2 of 2-by-2 unitary matrices relative to a quadratic p-adic field extension, we explain how to use the internal structure of its Langlands parameter to construct a underlying type of this representation. (If time permits, we will also cover a construction of discrete series representations.)

Discussion of the final touches on combined paper (erstwhile, Parts 1 and 2), now called _Arthur packets by way of microlocal vanishing cycles of perverse sheaves, with examples_.

We've encountered three interesting twists: one that appears when we normalise the microlocal vanishing cycles functor; one that appears when we relate the Fourier transform to microlocal vanishing cycles; and one that appears when we compare Moeglin's normalisation of Arthur packets with Arthur's normalisation. Today we wonder why they all coincide in our examples, and try to understand how they relate more generally.