Video Lectures

We consider the problem of approximately solving a system of homogeneous linear equations over reals, where each equation contains at most three variables. Since the all-zero assignment always satisfies all the equations exactly, we restrict the...

Paul Atewell, Leon Levy Foundation Member, School of Social Science. In the United States, ever-increasing proportions of high school graduates continue into college, and more and more undergraduates continue into master’s programs. One concern with...

*It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard for their own interest. Each participant in a competitive economy is led by an invisible hand to promote an end which was no...

Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the Glauber dynamics for the Ising model on Z2 everywhere except at criticality. While the critical behavior of the Ising model has long...

The cover time of a graph is one of the most basic and well-studied properties of the simple random walk, and yet a number of fundamental questions concerning cover times have remained open. We show that there is a deep connection between cover...

The ordinary homology of a subset S of Euclidean space depends only on its topology. By systematically organizing homology of neighborhoods of S, we get quantities that measure the shape of S, rather than just its topology. These quantities can be...

In this talk we will present a near-optimal compression scheme for bounded-round randomized 2-party communication protocols. Previously, such a scheme was only known for protocols where the inputs to the parties are independent. The results yield a...

We give a simple combinatorial proof of the Chernoff-Hoeffding concentration
bound for sums of independent Boolean random variables. Unlike the standard
proofs, our proof does not rely on the method of higher moments, but rather uses
an intuitive...

Semidefinite programming bounds are widely used in combinatorial optimization, quantum computing and complexity theory. The first semidefinite programming bound to gain fame is the so-called theta number developed by Lov\'asz to compute the Shannon...