Previous Conferences & Workshops

We consider questions that arise naturally from the subject of the first talk. The have two main results: 1. In genus $g$, the algebraic degrees of pseudo-Anosov stretch factors include all even numbers between $2$ and $6g - 6$; 2. The Galois...

In this first talk, we give an introduction to Penner’s construction of pseudo-Anosov mapping classes. Penner conjectured that all pseudo-Anosov maps arise from this construction up to finite power. We give an elementary proof (joint with Hyunshik...

Powerful theorems of Thurston, Perelman, and Mostow tell us that almost every 3-dimensional manifold admits a hyperbolic metric, and that this metric is unique. Thus, in principle, there is a 1-to-1 correspondence between a combinatorial description...

In the second lecture, I will discuss several natural geometric flows defined on bundles over the moduli spaces of curves. I will describe basic ergodic properties of these flows. I will discuss some open questions and some of the progress made in...

Reeder and Yu gave recently a new construction of certain supercuspidal representations of $p$-adic reductive groups (called epipelagic representations). Their construction relies on the existence of stable vectors in the first Moy-Prasad filtration...

We show an exponential gap between communication complexity and external information complexity, by analyzing a communication task suggested as a candidate by Braverman [Bra13]. Previously, only a separation of communication complexity and internal...

The first lecture will give some background on the geometry and dynamics on hyperbolic surfaces. I will give a brief overview of Teichmüller theory and properties of the mapping class groups and the space of geodesic currents. I will discuss some...

A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a log...

Many polynomial-time solvable (combinatorial) optimization problems can be reduced to the feasibility problem and the intersection problem. In this talk, I will present the first nearly cubic time algorithm for both problems using a new cutting...