Speaker: Sergey Galkin

Title: Mirrors for Mori and Mukai

Date: Jun 2, 2011, 10:30 - 13:00

Place: Room 204, RIMS, Kyoto

There are only finitely many deformation classes of Fano manifolds in any given dimension, and the list of threefolds is known thanks to Fano, Iskovskikh, Mori and Mukai. Based on ideas from mirror symmetry, we develop an algorithm to list Fano varieties in any given dimension, in particular we were able to recover the known classification of 3-folds. Besides we provide explicit descriptions for Fano threefolds as ("unabelianizations" of) complete intersections in toric manifolds, and thus we compute their Gromov-Witten invariants and prove the mirror symmetry hypothesis. It is a report on the joint project "Fano Varieties and Extremal Laurent Polynomials" with T.Coates, A.Corti, V.Golyshev and A.Kasprzyk (fanosearch.net). I'll review some amusing corollaries of this work, along with further observations and speculations on the next day.