Are factors of sparse polynomials sparse? This is a really basic
question and we are still quite far from understanding it in
general. In this talk, I will discuss a recent result showing that
this is in some sense true for multivariate polynomials...
Kazhdan–Lusztig (KL) polynomials for Coxeter groups were
introduced in the 1970s, providing deep relationships among
representation theory, geometry, and combinatorics. In 2016, Elias,
Proudfoot, and Wakefield defined analogous polynomials in
the...
In the early 1930's, the Ergodic theorems of von Neumann and
Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms,
and the natural question was born: is ergodicity the "general case"
among conservative dynamical systems? Oxtoby and Ulam...
Constraint satisfaction problems (CSPs) are a central topic of
study in computer science. A fundamental question about CSPs is as
follows. Given a CSP where each constraint has the form of some
predicate P and almost all of the constraints can be...
We consider a reaction-diffusion equation with a nonlocal
reaction term. This PDE arises as a model in evolutionary ecology.
We study the regularity properties and asymptotic behavior of its
solutions.
I will discuss joint work with Hutchings which constructs
nonequivariant and a family floer equivariant version of contact
homology. Both theories are generated by two copies of each Reeb
orbit over Z and capture interesting torsion information. I...
I will present a proof with some substantial details of the
Multiplicity One Conjecture in Min-max theory, raised by Marques
and Neves. It says that in a closed manifold of dimension between 3
and 7 with a bumpy metric, the min-max minimal...
In this talk I want to discuss two related questions about the
variational structure of the Yang-Mills functional in dimension
four. The first is the question of 'gap' estimates; i.e.,
determining an energy threshold below which any solution
must...
I will give a tour of some of the key concepts and ideas in
proof complexity. First, I will define all standard propositional
proof systems using the sequent calculus which gives rise to a
clean characterization of proofs as computationally limited...
I will discuss some current joint work with Helmut Hofer, in
which we define and establish properties of a new class of
pseudoholomorhic curves (feral J-curves) to study certain
divergence free flows in dimension three. In particular, we show
that...
