Video Lectures

The signature of a knot K in the 3-sphere is a classical  invariant that gives a lower bound on the genera of compact oriented surfaces in the 4-ball with boundary K. We say that K is hyperbolic if its complement admits a complete, finite volume...

Proving a 2009 conjecture of Itai Benjamini, we show:  For any C, there is a greater than 0 such that for any simple random walk on an n-vertex graph G, the probability that the first Cn steps of the walk hit every vertex of G is at most exp[-an]. ...

Polyhedral Liouville domains

Marco Castronovo

I will explain the construction of a new class of Liouville domains that live in a complex torus of arbitrary dimension, whose boundary dynamics encodes information about the singularities of a toric compactification. The primary motivation for this...