We give an elementary proof of a generalization of Bourgain and
Tzafriri's Restricted Invertibility Theorem, which says roughly
that any matrix with columns of unit length and bounded operator
norm has a large coordinate subspace on which it is well...
Let H be a fixed graph with h vertices. The graph removal lemma
states that every graph on n vertices with o(nh) copies of H can be
made H-free by removing o(n2) edges. We give a new proof which
avoids Szemeredi's regularity lemma and...
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...
