I will first give an overview of ECH. Then I will describe how
to compute ECH in the Morse-Bott setting a la Bourgeois. I will
discuss some classes of examples where this approach works. Finally
I will sketch the gluing results that allow us to...
The theory of "random surfaces" has emerged in recent decades as
a significant field of mathematics, lying somehow at the interface
between geometry, probability, and mathematical physics. I will
give a friendly (I hope) colloquium-level overview of...
Sampling from high-dimensional, multimodal distributions is a
computationally challenging and fundamental task. This talk
will focus on a family of random instances of such problems
described by random quadratic potentials on the hypercube known
as...
Weinstein domains and their symplectic invariants have been
extensively studied over the last 30 years. Little is known about
non-Weinstein Liouville domains, whose first instance is due to
McDuff. I will describe two key examples of such domains in...
I will motivate the study of coproducts and describe a new
coproduct structure on the symplectic cohomology of Liouville
manifolds. Time permitting, I will indicate how to compute it in an
example to show that it's not trivial. This is based on my...
I will discuss how the Deligne-Mumford compactification of
curves arises from the uncompactified moduli spaces of curves as a
result of some algebraic operations related to (pr)operadic
structures on the moduli spaces. I will describe how a...
If a set of integers is syndetic (finitely many translates cover
the integers), must it contain two integers whose ratio is a
square? No one knows. In the broader context of the
disjointness between additive and multiplicative configurations
and...
A powerful technique developed and extended in the past decade
in communication complexity is the so-called "lifting
theorems." The idea is to translate the hardness results from
"easier" models, e.g., query complexity, polynomial degrees, to
the...
AGN feedback is now widely considered to be one of the main
drivers in regulating the growth of massive galaxies. In my talk I
will describe several efforts in our group to understand the power,
reach and impact of AGN feedback processes. We find...
Symmetries of Quantum Field Theories (QFTs), whose fusion does
not satisfy a group multiplication law, are generally referred to
as non-invertible. I will discuss their connection to generalized
gauging and higher fusion categories, providing by...
