Speaker: Sarah Dijols,
The Generalized Injectivity Conjecture of CasselmanShahidi states that the unique irreducible generic subquotient of a (generic) standard module is necessarily a subrepresentation. It is related
to Lfunctions, as studied by Shahidi, hence has some numbertheoretical flavor, although our technics lie in the fields of representations of reductive groups over local fields. It was proven for classical groups (SO(2n+1), Sp2n, SO(2n)) by M.Hanzer in 2010. In this talk, I will first explain our interest in this conjecture, and describe its main ingredients. I will further present our proof (under some restrictions) which uses techniques more amenable to prove this conjecture for all quasisplit groups.
Event Date: Thursday, October 4, 2018  10:00 to 11:30

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 Lfunction of GL(3). Then I will report my recent work joint with J. Hundley on the holomorphy of adjoint Lfunction of GL(3). The second integral gives an integral representation of standard Lfunction of G2 itself. Related to this integral, we can consider a FourierJacobi model for G2. I will discuss recent work joint with B. Liu on the uniqueness of such models over finite fields.
Event Date: Thursday, September 20, 2018  10:00 to 11:30

Event Date: Sunday, August 12, 2018  09:00 to Saturday, August 18, 2018  17:00

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 KashiwaraSaito singularity. While the 1997 paper showed that the characteristic cycles of the KashiwaraSaito 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 padic GL(16) with the property that its ABVpacket (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 KashiwaraSaito representation of GL(16) and to \pi' as its coronal representation. This will provide the smallest known example of an irreducible representation of padic general linear group with one coronal representation.
Locations: Zoom (https://zoom.us/j/238450154), Calgary, Lethbridge
Event Date: Tuesday, July 24, 2018  10:00 to 11:30

Locations: Zoom, Calgary, Paris, Lethbridge
Event Date: Thursday, July 19, 2018  10:00 to 11:30

Andrew, Bin and Clifton
Zoom, Lethbridge, Beijing and Calgary
Event Date: Monday, May 28, 2018  19:00 to 20:00

Speaker: Andrew Fiori
Location: Zoom, Paris, Calgary and Lethbridge
Event Date: Thursday, May 10, 2018  09:00 to 10:30

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
Event Date: Monday, May 7, 2018  19:00 to 20:30

Topic: How to enumerate all stata in Vogan varieties for GL(n). Quivers perspective.
Some observations about the KashiwaraSaito singularity in the Vogan variety for GL(16).
Speaker: Reginald Lybbert
Location: Calgary, MS337
Event Date: Friday, May 4, 2018  10:00 to 11:30

Overview of the Voganish Project
Statement of summer objectives: Microlocal vanishing cycles of the KashiwaraSaito singularity
Divide and conquer:
Nicole Kitt: Calculations using the Fourier transform
Reginald Lybbert: Calculations using resolution of singularities
Location: University of Calgary, MS 337
Event Date: Tuesday, May 1, 2018  10:00 to 11:30
