The famous theorem of Szemerédi says that for any natural number
$k$ and any $a > 0$ there exists n such that if $N >= n$ then
any subset $A$ of the set $[N] ={1,2,...,N}$ of size $|A| >= a$
$N$ contains an arithmetic progression of length $k$. We...
Let F be a locally compact non-Archimedean field, p its residue
characteristic and G a connected reductive algebraic group over F .
The classical Satake isomorphism describes the Hecke algebra (over
the field of complex numbers) of double...
I will outline the proof of various cases of the local-global
compatibility statement alluded to in the title, and also explain
its applications to the Fontaine--Mazur conjecture, and to a
conjecture of Kisin.
I will outline the proof of various cases of the local-global
compatibility statement alluded to in the title, and also explain
its applications to the Fontaine—Mazur conjecture, and to a
conjecture of Kisin.
The d-divisible partition lattice is the collection of all
partitions of an n-element set where each block size is divisible
by d. Stanley showed that the Mobius
function of the d-divisible partition lattice is given (up to a
sign) by the number...
The firefighter problem is a monotone dynamic process in graphs
that can be viewed as modeling the use of a limited supply of
vaccinations to stop the spread of an epidemic. In more detail, a
fire spreads through a graph, from burning vertices to...
Let $f(x_1,...,x_n)$ be a low degree polynomial over $F_p$. I
will prove that there always exists a small set $S$ of variables,
such that `most` Fourier coefficients of $f$ contain some variable
from the set $S$. As an application, we will get a...
I will introduce Shimura varieties and discuss the role they
play in the conjectural relashionship between Galois
representations and automorphic forms. I will explain what is meant
by a geometric realization of Langlands correspondences, and...
In our work we study the structure of polynomials of degree
three and four that have high bias or high Gowers norm, over
arbitrary prime fields. In particular we obtain the following
results.
We give a canonical representation for degree three or...
