Speaker
Atsushi Takahashi
Description
For ADE singularities, Deligne gave a characterization of sets of distinguished bases and a recursion relation for their cardinalities, and proved Looijenga's conjecture on their coincidence with the degrees of Lyashko-Looijenga maps which capture topological information of bifurcation sets. Categorifying distinguished bases into full exceptional collections in derived directed Fukaya categories motivated by the idea of homological mirror symmetry, I'll explain how Deligne's recursion and comparison of degrees of Lyashko-Looijenga map with numbers of full exceptional collections can be naturally generalized.
