Physics inspired mathematics helps us understand the random
evolution of Markov processes. For example, the Kolmogorov forward
and backward differential equations that govern the dynamics of
Markov transition probabilities are analogous to the...
I will explain that incompressible Navier-Stokes is the wrong
equation to describe turbulence in low Mach number molecular fluids
because it neglects the effects of thermal noise. There should, in
fact, be strong effects of thermal noise throughout...
We present an elementary summary of known results, and open
questions, on scaling problems in hydrodynamic turbulence in three
dimensions. The goal is to provide some background for the two
talks to follow, and summarize Victor Yakhot's theory...
I will explain the construction of a functor from the exact
symplectic cobordism category to a totally ordered set, which
measures the complexity of the contact structure. Those invariants
are derived from a bi-Lie infinity formalism of the rational...
Motivated by a formal similarity between the Hard Lefschetz
theorem and the geometric Satake equivalence we study vector spaces
that are graded by a weight lattice and are endowed with linear
operators in simple root directions. We allow field...
In his seminal paper from 1973, Garland introduced a machinery
for proving vanishing of group cohomology for groups acting on
Bruhat-Tits buildings. This machinery, known today as “Garland’s
method”, had several applications as a tool for proving...
Expander graphs in general, and Ramanujan graphs in particular,
have played an important role in computer science and pure
mathematics in the last four decades. In recent years the area of
high dimensional expanders (i.e. simplical complexes with...
A recent line of work has focused on the following question: Can
one prove strong unconditional lower bounds on the number of
samples needed for learning under memory constraints? We study an
extractor-based approach to proving such bounds for a...
We will discuss recent developments of the theory of
a-contraction with shifts to study the stability of discontinuous
solutions of systems of equations modeling inviscid compressible
flows, like the compressible Euler equation.
