Event Details

Speaker: Danil Koževnikov (Edinburgh)

Title: Skeleta of complete intersections and mirror symmetry

Abstract: Homological mirror symmetry is a conjecture due to Maxim Kontsevich, predicting an equivalence between the derived category of coherent sheaves of an algebraic variety X and the Fukaya category of the “mirror” symplectic manifold Y. One of the most notable mirror constructions are Batyrev-Borisov mirrors, where both spaces are presented as complete intersections inside toric varieties, which means that a lot of their properties can be understood in purely combinatorial terms. In this talk, I will discuss some new results concerning Lagrangian skeleta of complete intersections in (C*)^n and explain how they could be used as the first step towards proving HMS for general Batyrev-Borisov pairs, following an approach that has already been applied in several special cases.