Title: The generalized doublingmethod and its applications
Abstract: The doubling method,first introduced by Piatetski-Shapiro and Rallis in the 80s, has had numerousapplications, e.g. to the theta correspondence and to arithmetic problems.In a series of recent works this method was generalized in severalaspects, with an application to functoriality from classical groups to GL(N).The most recent result is a multiplicityone theorem (joint work with Gourevitch and Aizenbud).
I will brieflysurvey the method and talk about some of its applications.

See the link http://math.huji.ac.il/~shnidman/HBWA.html

This semester will be devoted to resolution of singularities -- a process that modifies varieties at the singular locus so that the resulting variety becomes smooth. For many years this topic had the reputation of very technical and complicated, though rather elementary.
In fact, the same resolution algorithm can be described in various settings, including schemes, algebraic varieties or complex analytic spaces.

Title: Mordell-Lang and Integral Points on Abelian Varieties in Characteristic p

Title: The tame site

This semester will be devoted to resolution of singularities -- a process that modifies varieties at the singular locus so that the resulting variety becomes smooth. For many years this topic had the reputation of very technical and complicated, though rather elementary.
In fact, the same resolution algorithm can be described in various settings, including schemes, algebraic varieties or complex analytic spaces.

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