In the representation theory of reductive p-adic groups, a lot of general structure was developed by Bernstein: supercuspidal representations, cuspidal support, Bernstein components and so on.

Let G be the group SL(2) over a finite extension F of Q_p, p odd. For a fixed r ≥ 0, we identify the elements of the Bernstein center of G supported in the Moy-Prasad G-domain G_{r^+}, by characterizing them spectrally. We study the behavior of convolution with such elements on orbital integrals of functions in C^∞_c(G(F)), proving results in the spirit of semisimple descent. These are ‘depth r versions’ of results proved for general reductive groups by J.-F. Dat, R. Bezrukavnikov, A. Braverman and D. Kazhdan.

I will finish the theory of Lubin-Tate, and start the last topic of this series -- Drinfeld's elliptic modules and CFT of function fields.

Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"

Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"

Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"

Title: Title: Self maps of varieties over finite fields Abstract: Esnault and Srinivas proved that as in Betti cohomology over the complex numbers, the value of the entropy of an automorphism of a smooth proper surface over a finite field $\F_q$ is taken in the subspace spanned by algebraic cycles inside $\ell$-adic cohomology. In this talk we will discuss some analogous questions in higher dimensions motivated by their results and techniques.

I'll tell a couple of anecdotes related to imaginary quadratic fields (e.g. primes in the sequence n^2+n+41), and then open a new story -- local CFT and the explicit construction of K^ab due to Lubin-Tate.

We'll talk about explicit class field theory of imaginary quadratic fields

Abstract: Any birational geometer would agree that the best algorithm for resolution of singularities should run by defining a simple invariant of the singularity and iteratively blowing up its maximality locus. The only problem is that already the famous example of Whitney umbrella shows that this is impossible, and all methods following Hironaka had to use some history and resulted in more complicated algorithms. Nevertheless, in a recent work with Abramovich and Wlodarczyk we did construct such an algorithm, and an independent description of a similar

Title: An intrinsic characterization of cofree representations of reductive groups

Abstract: Any birational geometer would agree that the best algorithm for resolution of singularities should run by defining a simple invariant of the singularity and iteratively blowing up its maximality locus. The only problem is that already the famous example of Whitney umbrella shows that this is impossible, and all methods following Hironaka had to use some history and resulted in more complicated algorithms. Nevertheless, in a recent work with Abramovich and Wlodarczyk we did construct such an algorithm, and an independent description of a similar

Geometric class field theory is an analog of the classical class field theory over function fields in which functions are replaced by sheaves. In the first part of my talk, I will formulate the result and explain its proof over C (the field of complex numbers).  

In the  second part of the talk, I will try to outline the proof in the case of finite fields and indicate how this result implies the classical unramified global class field theory over function fields. 

Most of the talk will be independent of the first one. 

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. P.S. Michael will continue his series of lectures on May 6.

Old and new on the de Rham-Witt complex

Abstract: After reviewing the definition and the basic properties of the de Rham-Witt complex for smooth schemes over a perfect field, I will discuss the new approach to the subject developed by Bhatt, Lurie and Mathew.

I will explain the main results and sketch work in progress on the problems raised by this theory.