Repeats every week every Sunday until Sat Jun 29 2019 except Sun Apr 21 2019.
11:00am to 1:00pm
Zlil Sela and Alex Lubotzky "Model theory of groups"
In the first part of the course we will present some of the main results in the theory of free,
hyperbolic and related groups, many of which appear as lattices in rank one simple Lie groups
We will present some of the main objects that are used in studying the theory of these groups,
and at least sketch the proofs of some of the main theorems.
In the second part of the course, we will talk about the model theory of lattices in high rank simple Lie groups.
Repeats every week every Sunday until Sun Jun 23 2019 except Sun Apr 21 2019.
2:00pm to 4:00pm
Yun and Zhang compute the Taylor series expansion of an automorphic L-function over a function field, in terms of intersection pairings of certain algebraic cycles on the so-called moduli stack of shtukas. This generalizes the Waldspurger and Gross-Zagier formulas, which concern the first two coefficients.
The goal of the seminar is to develop the background necessary to state their formula, and then indicate the structure of the proof. If time allows, we may also discuss applications to the Birch and Swinnerton-Dyer conjecture for elliptic curves over function fields.
In a series of 2 talks I will try to explain that in the function field case the unramified global class
field theory has a simple geometric interpretation and a conceptual proof. We will only consider the unramified case (see, for example, https://arxiv.org/pdf/1507.00104.pdf or https://dspace.library.uu.nl/handle/1874/206061)
Key words: Abel-Jacobi map, l-adic sheaves, sheaf-function correspondence.
Repeats every week every Monday until Mon Apr 29 2019 except Mon Apr 22 2019.
4:00pm to 6:00pm
Location:
Ross 70
Abstract. This is a joint work with Linhui Shen.
A decorated surface is an oriented surface with punctures and a finite collection of special points on the boundary, considered modulo isotopy.
Let G be a split adjoint group. We introduce a moduli space Loc(G,S) of G-local systems on a decorated surface S, which reduces to the character variety when S has no boundary, and quantize it.
