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...
In this talk, I will elaborate on the main technical component
of our PCP—the construction of routing protocols on
high-dimensional expanders (HDX) that can withstand a constant
fraction of edge corruptions. We consider the following routing
problem...
The theory of probabilistically checkable proofs (PCPs) shows
how to encode a proof for any theorem into a format where the
theorem's correctness can be verified by making only a constant
number of queries to the proof. The PCP Theorem [ALMSS] is a...
Recent progress on character bounds for groups of Lie type makes
it feasible in many cases to find the asymptotic growth, for fixed
q and n tending to infinity, of the number of n-dimensional
representations of a Fuchsian group G over the field with...
