UT - math Calendar

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3:45 pm Tuesday, December 10, 2019
Junior Geometry: Divisors on the moduli space of genus zero curves

by George D. Torres (UT Austin) in RLM 12.166

Given a smooth variety X, the divisors (~ codimension 1 subarieties) encode geometric information about X and are often easier to work with than X itself. This talk will be about the divisors on the variety M_{0,n}, the moduli space of genus zero pointed curves. I will state the complete characterization of these divisors due to Keel as well as a combinatorial way to view them. With a little tropical geometry, we will also see that the closure of M_{0,n} embeds into the toric variety of phylogenetic trees. Time permitting, I will demonstrate how the combinatorial view can be used to prove hard theorems about M_{0,n}, such as the Symmetric F-Conjecture

1:30 pm Wednesday, December 11, 2019
Geometry Seminar: Branes And Interfaces For 2D Landau-Ginzburg Models With Twisted Masses

by Greg Moore (Rutgers University) in RLM 10.176

This talk will be a progress report on work in progress with Ahsan Khan. The ultimate goal of the project is to understand a ``categorification'' of BPS indices (and their wall-crossing) in both two and four dimensional supersymmetric QFT. In 2015 Gaiotto, Moore, and Witten (GMW) approached the problem of the categorification of BPS indices in massive two-dimensional models with (2,2) supersymmetry by constructing an A-infinity 2-category of interfaces (aka domain walls) between such theories using a ``web formalism.'' An important first step in generalizing to 2d-4d systems is to incorporate ``twisted masses'' into the two-dimensional setting. The talk will describe some results on the generalization of the GMW discussion to include twisted masses. NOTE the special time and location.