Video Lectures

In 2007, Zeev Dvir shocked experts by giving a one-page proof of the finite field Kakeya problem. The new idea in the proof was to introduce high degree polynomials into a problem about points and lines. This idea has led to progress on several...

There are two important measures of the complexity of a boolean function: the sensitivity and block sensitivity. Whether or not they are polynomial related remains a major open question. In this talk I will survey some known results on this...

fundamental theorem in linear algebra is that any real n x d matrix has a singular value decomposition (SVD). Several important numerical linear algebra problems can be solved efficiently once the SVD of an input matrix is computed: e.g. least...

We discuss three areas of algorithmic game theory that have grappled with intractability. The first is the complexity of computing game-theoretic equilibria, like Nash equilibria. There is an urgent need for new ideas on this topic, to enable...

Persistent homology is a central object of study in applied topology. It offers a flexible framework for defining invariants, called barcodes, of point cloud data and of real valued functions. Many of the key results of the last several years in the...

We will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further...