New types of symmetries have been considered in algebra and
algebraic geometry and a higher analog of representation theory has
been developed to answer questions of classical representation
theory. Geometric representation theory can be viewed as...
For a fixed integer k > 1, the Boolean k-XOR problem consists
of a system of linear equations mod 2 with each equation involving
exactly k variables. We give an algorithm to strongly refute
*semi-random* instances of the Boolean k-XOR problem on n...
The physicist Abrikosov predicted that in certain
superconductors, one should observe triangular lattices of
vortices, now called Abrikosov lattices. When studying ground
states of Coulomb gases, which is motivated by questions in
In this talk, I will give an overview of some recent results
motivated by the computation and applications of persistent
homology, a theory that creates a bridge between the continuous
world of topology and the discrete world of data, and...
The group of Hamiltonian diffeomorphisms of a symplectic
manifold admits a remarkable bi-invariant metric, called
Hofer’s metric. My talk will be about a recent joint work
with Dan Cristofaro-Gardiner and Vincent Humilière resolving
A discrete countable group is matricially stable if its finite
dimensional approximate unitary representations are perturbable to
genuine representations in the point-norm topology. We aim to
explain in accessible terms why matricial stability for a...
This talk introduces a directed analog of the
classical Laplacian matrix and discusses algorithms for
solving certain problems related to them. Of particular interest is
that using such algorithms, one can compute the stationary
distribution of a...