Algebra and Geometry Seminar

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, in which we construct a compactificatio​n 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-MacPhers​on compactificatio​n for pairs of spaces.