Video Lectures

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We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function arguments to...
Random graphs and expander graphs can be viewed as sparse approximations of complete graphs, with Ramanujan expanders providing the best possible approximations. We formalize this notion of approximation and ask how well an arbitrary graph can be...
We introduce a new method of obtaining sharp estimates on mixing for Glauber dynamics for the Ising model, which, in particular, establishes cutoff in three dimensions up to criticality. The new framework, which considers ``information percolation''...
After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold \((M, \omega)\) is a symplectic invariant that measures, roughly speaking, the size of the...
"All This Has Come Upon Us" is a collection of archival pigment prints by Mark Podwal, a selection of which is on display, which illustrate the tragedies and injustices suffered by the Jewish people. Each work, conceived as a page of a book...