Abstract: In this talk, I will present some new results about skeleta of complete intersections inside (C*)^n. I will start by briefly reviewing the Batyrev-Borisov mirror construction, which uses combinatorial dualities between lattice polytopes to produce mirror pairs of Calabi-Yau complete intersections in Fano toric varieties. The main focus of the talk will be open Batyrev-Borisov complete intersections (…

Abstract: I will discuss the construction of Symplectic Lefschetz fibrations
using tools from classical Lie theory, and then explain how they were used
to provide examples of existence/nonexistence of Mirrors having the
prescribed categories of coherent sheaves and of singularities.