Monday, October 1, 2018
Time  Items 

All day 

4:00pm 
10/01/2018  4:15pm Abstract: Given a translation surface there is a circle of directions in which one might apply Teichmuller geodesic flow. We will describe work showing that for every (not just almost every!) translation surface the set of directions in which Teichmuller geodesic flow diverges on average  i.e. spends asymptotically zero percent of its time in any compact set  is 1/2. In the first part of the talk, we will recall work of Masur, which connects divergence of Teichmuller geodesic flow with nonunique ergodicity of straightline flow on the translation surface. We will then review the continued fraction case and mention related work of Kadyrov, Kleinbock, Lindenstrauss, and Margulis in the homogenous setting. In the second part of the talk, we will describe the lower bound (joint with H. Masur) and how it depends on (1) a quantitative recurrence result for Teichmuller geodesic flow and (2) the quadratic growth of cylinders on translation surfaces. In the third and final part of the talk, we will describe the upper bound (joint with H. alSaqban, A. Erchenko, O. Khalil, S. Mirzadeh, and C. Uyanik), which adapts the argument of Kadyrov, Kleinbock, Lindenstrauss, and Margulis to the Teichmuller geodesic flow setting using Margulis functions. Time permitting we will also describe work which shows that for any compactlysupported continuous function the set of directions for which the timeaverages along the flow deviate from the spaceaverage by a fixed definite amount have Hausdorff dimension strictly less than one. Location:
LOM 206
10/01/2018  4:30pm Over the past two decades, Vertex Operator Algebras (VOA) have appeared in various contexts related to supersymmetric quantum field theories. I will discuss a class of VOAs arising from local operators at junctions of interfaces in the maximally symmetric fourdimensional gauge theory. The simplest trivalent junction is associated to a threeparameter family of VOAs (corner/vertex VOAs) generalizing wellknown $W_N$algebras. Vertex VOAs can be used to engineer more complicated VOAs associated to any web of trivalent junction by a gluing procedure. This construction provides us with an intuitive, pictorial way to construct and study VOAs. At the level of characters, the gluing procedure mimics the topological vertex construction of DT invariants for toric CalabiYau threefolds motivating the name “vertex VOA”. As an application of the newly constructed VOAs, I will propose a generalization of the AGT correspondence relating $W_N$algebras and moduli spaces of instantons on $\mathbb{C}^2$ to the web algebras.
Location:
LOM 214
