The question of asbolute continuity, with respect to the
reference measure, of the harmonic measure on a domain with rough
boundary has been the object of many important results. Here we ask
about the similar question, but where the Dirichlet...
Symplectic manifolds exhibit curious behaviour at the interface
of rigidity and flexibility. A non-squeezing phenomenon discovered
by Gromov in the 1980s was the first manifestation of this. Since
then, extensive research has been carried out into...
The Brunn-Minkowski inequality is a fundamental result in convex
geometry controlling the volume of the sum of subsets of ℝn.
It asserts that for sets A,B⊂ℝn of equal volume and a
parameter t∈(0,1), we have |tA+(1−t)B|≥|A| with equality iff A=B
is...
The analytic de Rham stack is a new construction in Analytic
Geometry whose theory of quasi-coherent sheaves encodes a notion of
p-adic D-modules. It has the virtue that can be defined even under
lack of differentials (eg. for perfectoid spaces or...
Recent advancements in quantum error correction have led to
breakthroughs in good quantum low-density parity-check (qLDPC)
codes, which offer asymptotically optimal code rates and distances.
However, several open questions remain, including the...
The study of the topology of hyperplane arrangement complements
has long been a central part of combinatorial algebraic geometry. I
will talk about intersection pairings on the twisted (co)homology
for a hyperplane arrangement complement, first...
I will motivate the study of the Schubert variety of a pair of
linear spaces via Kempf collapsing of vector bundles. I'll describe
equations defining this variety and how this yields a simplicial
complex determined by a pair of matroids which...
I will describe the duality of incompressible Navier-Stokes
fluid dynamics in three dimensions, leading to its reformulation in
terms of a one-dimensional momentum loop equation.
The decaying turbulence is a solution of this equation
equivalent to a...
I will introduce a new structure on (relative) Symplectic
Cohomology defined in terms of a PROP called the “Plumber’s PROP.”
This PROP consists of nodal Riemann surfaces, of all genera and
with multiple inputs and outputs, satisfying a condition...
