Al Kasprzyk (Nottingham, UK) will talk in the geometry seminar, on Tuesday 11th October. His title is *“The combinatorics of mirror symmetry”* and his abstract is below. The talk will be in the Salle de Profs (9th floor building NO) at 2pm. (Note the seminar is a double bill on the 11th, with a talk by Laurent Schwachhöfer on *“Cohomological invariants of G2 and Spin(7) manifolds”* afterwards.)

Recent progress in understanding Mirror Symmetry for Fano manifolds by Coates, Corti, and myself is closely connected with the combinatorics of lattice polytopes. Although many of the motivating ideas remain conjectures, this new view-point is making significant and unexpected contributions to both the theory of lattice polytopes, and to how we may approach the classification of Fano varieties. I hope to sketch these ideas, justify what we expect in higher dimensions, and explain some of the main challenges.