This week's seminar is given by Jakob Hultgren, Umeå universitet.
Title: Mirror Symmetry and Combinatorial Aspects of Complex Geometry
Abstract: Mirror Symmetry is a mysterious duality in algebraic geometry, originally discovered by physicists in the 1980's. An attempt to (at least conceptually) reduce mirror symmetry to a simpler duality of a more combinatorial nature leads to the SYZ-conjecture from 1996. I will present results about this conjecture in a setting where the combinatorial duality dictated by SYZ is just duality of polytopes and outline some ideas on how the results can be extended to more general settings. These ideas involve certain "polarized" simplicial complexes and a pairing on these akin to the usual pairing on finite dimensional vector spaces and their duals.
Based on joint work with Rolf Andreasson, Thibaut Delcroix, Mattias Jonsson, Enrica Mazzon and Nick McCleerey.
