16.30 - 17.30 @ HGD 2201

Jingsong Chai

(Sun Yat-sen University)

(Sun Yat-sen University)

On Poisson Summation Formula and Functional Equations of L-functions

In this talk we first review Poisson summation formula on GL(n) and its application to global functional equation in Godement-Jacquet integrals. We then discuss potential applications of such summation formula to derive global functional equations in other integral representations of L-functions.

15.00 - 16.00 @ HGD 2201

Bin Xu

(Sichuan University)

(Sichuan University)

A reciprocal problem of Gan-Gross-Prasad conjectures with an approach via twisted descent method

In this talk, we will introduce a reciprocal problem of the Gan-Gross-Prasad conjectures, and explain an approach using the twisted descent method. In particular, we will give both local and global examples in the case of special orthogonal groups.

13.30 - 14.30 @ HGD 2201

Voronoi formulas for automorphic forms on GL(N)

Automorphic forms are well-behaved functions on a group (such as GL(n,R)) which are invariant under the action of a discrete arithmetic subgroup (such as SL(n,Z)). They encode vital arithmetic information. Voronoi formulas are Poisson-style summation formulas for automorphic forms. They have been powerful tools in analytic number theory for a long time (with applications to the divisor problem, the circle problem, subconvexity of L-functions, etc). I will talk about Voronoi formulas and their recent development and applications. Some results are joint work with Stephen D Miller, Eren M Kiral.

13.30 - 15.00 @ HGD 2213

Breuil-Kisin Windows and Ekedahl-Oort Stratifications of Shimura Varieties (3)

13.30 - 15.00 @ HGD 2213

Breuil-Kisin Windows and Ekedahl-Oort Stratifications of Shimura Varieties (2)

13.30 - 15.00 @ HGD 2213

Breuil-Kisin Windows and Ekedahl-Oort Stratifications of Shimura Varieties (1)

This talk is based on my Thesis. By constructing (non-canonical) deformations for the associated `p`-divisible groups of the special fibre `S` of a Shimura variety, we manage to construct a morphism from `S` to some quotient sheaf of the loop group associated with `S`. We show that the geometric fibre of this morphism gives back the Ekedahl-Oort strata of `S`: this also gives a conceptual interpretation of Viehmann's new invariant "elements of truncation of level one". I will recall the Ekedahl-Oort stratification of Shimura varieties (of good reduction) and the classification of `p`-divisible groups in terms of filtered Breuil-Kisin modules (or Breuil-Kisin windows, in my term), and then present the strategy of constructing the morphism aforementioned.

10.00 - 11.00 @ HGD 2201

A local trace formula for the Ginzburg-Rallis model and some generalizations

We will first discuss a local trace formula for the Ginzburg-Rallis
model. This trace formula allows us to prove a multiplicity formula for the
Ginzburg-Rallis model, which implies the multiplicity one theorem on the Vogan `L`-packet.
Then we will talk about some generalizations of this trace formula to other models.