Thursday: Jared Weinstein, 2 talks
Craig Citro
Jared Weinstein is going to be in town on Thursday and Friday this
week, and he'll give two talks on Thursday. Both talks are in
Padelford C-401, and we'll probably walk over to the Ave for lunch.
Here are the abstracts:
Title: The local Jacquet-Langlands correspondence via Fourier analysis
11AM-Noon
Abstract: Let $F$ be a nonarchimedean local field, and let $B$ be a
quaternion division algebra over $F$. The Jacquet-Langlands
correspondence is a bijection between certain representations of
$GL_2(F)$ and its twist $B^\times$. This correspondence, proved in
1970 by Jacquet and Langlands, preserves certain quantities called
$L$- and $\epsilon$-factors. We will present a new proof of this
result in which the preservation of these quantities is automatic from
the construction. We will reduce the problem to a Fourier-theoretic
calculation on finite groups.
Title: Nonabelian Lubin-Tate theory in the cohomology of smooth
curves in characteristic $p$.
2-3PM
Abstract: This is a continuation of the first talk. We explain how
both the Jacquet-Langlands correspondence (relating representations of
$GL_n(F)$ to those of a twist) and the local Langlands correspondence
for $GL_n$ (relating representations of $GL_n(F)$ to two-dimensional
Galois representations) can be realized simultaneously in the
cohomology of one geometric object. This program, known as nonabelian
Lubin-Tate theory,
was carried out successfully by Carayol in the case of $n=2$ in 1986.
Further progress was made in 2002 by Harris and Taylor for all $n$. We
will show how part of the correspondence in the $n=2$ case can be
realized ``explicitly" in the étale cohomology of a family of smooth
curves in characteristic $p$.
-cc