The "hard discs" model of matter has been studied intensely in
statistical mechanics and theoretical chemistry for decades. From
computer simulations it appears that there is a solid--liquid phase
transition once the relative area of the discs is...
A perfect matching in a k-uniform hypergraph H = (V, E) on n
vertices
is a set of n/k disjoint edges of H, while a fractional perfect
matching
in H is a function w : E → [0, 1] such that for each v ∈ V we
have
e∋v w(e) = 1. Given n ≥ 3 and 3 ≤ k ≤ n...
This talk will be a progress report on an ongoing research
project which is joint work with Ajay Chandra and Gianluca Guadagni
and which concerns a p-adic analog of the Brydges-Mitter-Scoppola
phi-4 model with...
Picard moduli spaces parametrize principally polarized abelian
varieties with complex multiplication by the ring of integers in an
imaginary-quadratic field. The loci where the abelian varieties
split off an elliptic curve in a controlled way are...
GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Some automorphic forms, despite the fact they are algebraic, do
not have any interpretation as cohomology classes on a Shimura
variety: therefore nothing is known at present on their
expected...
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...
