Speaker: Nick Sheridan (The University of Edinburgh) (Speical place and time, 2-361 , 4 pm - 5 pm)

Title: Homological mirror symmetry for Calabi-Yau hypersurfaces in toric varieties

Abstract:  Kontsevich's homological mirror symmetry conjecture predicts an equivalence between the derived category of coherent sheaves on one algebraic variety X, and the Fukaya category of a 'mirror' symplectic manifold Y. A broad class of conjectural mirror pairs (X,Y) of Calabi-Yau hypersurfaces in toric varieties was constructed by Batyrev. We prove Kontsevich's conjecture for a large subset of such Batyrev mirror pairs, in all but finitely many characteristics. The key ingredients are Gammage-Shende's proof of homological mirror symmetry 'at large volume' (which uses Ganatra-Pardon-Shende's work to reduce the computation of the Fukaya category to microlocal sheaf theory), and a deformation argument to a neighbourhood of the large volume limit using Seidel's relative Fukaya category. Based on joint work with Sheel Ganatra, Andrew Hanlon, Jeff Hicks, and Dan Pomerleano.