Video Lectures

Let \(G\) be a finite group, and let \(a\), \(b\), \(c\),... be independent random elements of \(G\), chosen at uniform distribution. What is the distribution of the element obtained by a fixed word in the letters \(a\), \(b\), \(c\),..., such as \...

The chromatic number \(k(G)\) of a graph \(G\) is always at least the size of its largest clique (denoted by \(w(G)\)), and there are graphs with \(w(G)=2\) and \(k(G)\) arbitrarily large. On the other hand, the perfect graph theorem asserts that if...

In this talk I will focus on two examples of K3 categories: bounded derived categories of (twisted) coherent sheaves and K3 categories associated with smooth cubic fourfolds. The group of autoequivalences of the former has been intensively studied...

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge...

This is joint work with Y. Canzani, B. Clarke, N. Kamran, L. Silberman and J. Taylor. We construct Gaussian measure on the manifold of Riemannian metrics with the fixed volume form. We show that diameter and Laplace eigenvalue and volume entropy...