A permutation pi=(pi_{1},...,pi_{n}) is consecutive 123-avoiding
if there is no sequence of the form pi_i pi_{i+1} pi_{i+2}. More
generally, for S a collection of permutations on m+1 elements, this
definition extends to define consecutive S...
In this expository talk, I will outline a plausible story of how
the study of congruences between modular forms of Serre and
Swinnerton-Dyer, which was inspired by Ramanujan's celebrated
congruences for his tau-function, led to the formulation of...
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...
