We consider a class of interacting particle systems with two
types, A and B which perform independent random walks at different
speeds. Type A particles turn into type B when they meet another
type B particle. This class of systems includes models...
Most of the visible matter in the Universe is a plasma, that is
a dilute gas of ions, electrons, and neutral atoms. In many
circumstances, the dynamics of this plasma can be modeled in the
continuum limit, using the equations of fluid mechanics...
We consider the Glauber dynamics (also called Gibbs sampling)
for sampling from a discrete distribution in high-dimensional space
(e.g., selecting a uniformly random legal coloring or independent
set in a given graph, or selecting a "typical" state...
Gross and Siebert have recently proposed an "intrinsic"
programme for studying mirror symmetry. In this talk, we will
discuss a symplectic interpretation of some of their ideas in the
setting of affine log Calabi-Yau varieties. Namely, we
describe...
Given a K3 surface XX over a number field KK, we
prove that the set of primes of KK where the geometric
Picard rank jumps is infinite, assuming that XX has
everywhere potentially good reduction. This result is formulated in
the general framework of...
A theorem of Bernstein identifies the center of the affine Hecke
algebra of a reductive group GG with the Grothendieck
ring of the tensor category of representations of the dual
group G∨G∨. Gaitsgory constructed a functor which
categrorifies this...
Some years ago, I proved with Shulman and Sørensen that
precisely 12 of the 17 wallpaper groups are matricially stable in
the operator norm. We did so as part of a general investigation of
when group C∗C∗-algebras have the semiprojectivity and
weak...
Expander graphs are graphs which simultaneously are both sparse
and highly connected. The theory of expander graphs received a lot
of attention in the past half a century, from both computer science
and mathematics. In recent years, a new theory of...
Valiant (1980) showed that general arithmetic circuits with
negation can be exponentially more powerful than monotone ones. We
give the first qualitative improvement to this classical result: we
construct a family of polynomials P-n in n variables...
