I will discuss the problem of determining the number of
infinite-volume ground states in the Edwards-Anderson (nearest
neighbor) spin glass model on $Z^D$ for $D \geq 2$. There are no
complete results for this problem even in $D=2$. I will focus
on...
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...
