# Geometry, Topology and Categorification Seminar: A compactified moduli space of pointed vertical lines in C^2

Monday, October 14 at 2:00pm to 3:00pm

This is a past event.

Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089

Nathaniel Bottman, USC

Abstract: A Lagrangian correspondence between symplectic manifolds induces a functor between their respective Fukaya categories. I will begin by introducing this construction, along with a family of abstract polytopes called 2-associahedra (introduced in math/1709.00119), which control the coherences among this collection of functors. Next, I will describe new joint work with Alexei Oblomkov (math/1910.02037), in which we construct a compactification of the moduli space of configurations of pointed vertical lines in $\mathbb{C}^2$ modulo affine transformations $(x,y) \mapsto (ax+b,ay+c)$. These spaces are proper complex varieties with toric lci singularities, which are equipped with forgetful maps to $\overline{M}_{0,r}$. I will describe some 2- and 3-dimensional examples, and indicate some future directions, including upcoming work to cast this as an instance of a version of Fulton-MacPherson compactification for pairs of spaces.

Event Type
Campus
Department
Mathematics