Video Lectures

A classical construction in topology associates to a space X and prime p, a new "localized" space Xp whose homotopy and homology groups are obtained from those of X by inverting p. In this talk, I will discuss a symplectic analog of this...

In this talk we will begin the discussion of the results in Bezrukavnikov's "On Two Geometric Realizations of the Affine Hecke algebra". We will put all the previous tools described in this series of talks together to construct the equivalence of...

Constraint metric approximation is about constructing an approximation of a group G, when the approximation is already given for a subgroup H. Similarly, constraint stability is about lifting a representation of a group G, when the lift is already...

Random sampling a subgraph of a graph is an important algorithmic technique.  Solving some problems on the (smaller) subgraph is naturally faster, and can give either a useful approximate answer, or sometimes even give a result that can be quickly...

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 approximation...

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 assigns...