Video Lectures

Abstract: Let Γ be a finitely generated subgroup of a compact group G. 1. I will recall what it means to say the action of Γ on G by left translation has spectral gap, and mention some examples and applications, e.g. Banach-Ruziewicz problem...

Schedule: https://sites.google.com/site/thingroups/schedule

In this talk we introduce the Apollonian group, sometimes coined the “quintessential” thin group, which is the underlying symmetry group of Apollonian circle packings. We review some of...

What is the distribution of the number of triangles in the random graph $G(n, 1/2)$? It was known for a long time that this distribution obeys a central limit theorem: from the point of view of large intervals (~ standard-deviation length), the...

Markoff numbers give rise to extremely low-lying reciprocal geodesics on the modular surface, but it is unknown whether infinitely many of these are fundamental, that is, the corresponding binary quadratic form has fundamental discriminant. In joint...

A classical property of pseudo-Anosov mapping classes is that they act on the space of projective measured laminations with north-south dynamics. This means that under iteration of such a mapping class, laminations converge exponentially quickly...

The Resolution proof system is perhaps the simplest and most universally used in verification system and automated theorem proving. It was introduced by Davis and Putnam in 1960. The study of its efficiency, both in terms of proof length of natural...

In this talk I will discuss some classical and new applications of the abc conjecture, its relation to conjectures about elliptic curves, and some (admittedly weak) unconditional partial results.

Tensor decompositions have been the key algorithmic components in provable learning of a wide range of hidden variable models such as topic models, Gaussian mixture models, independent component analysis, dictionary learning. Despite its success...

This is joint work with Thomas Barthelme of Penn State University. There are Anosov and pseudo-Anosov flows so that some orbits are freely homotopic to infinitely many other orbits. An Anosov flow is $R$-covered if either the stable or unstable...