Alexander Kasprzyk: The combinatorics of Mirror Symmetry

Recent work has focused on approaching the classification of Fano manifolds in three-dimensions via Mirror Symmetry. This has been extraordinarily successful, recovering the famous classification originally due to Mori and Mukai. As a consequence, a rich combinatorial structure has been exposed, highlighting a previously unanticipated connection with lattice polytopes and a new combinatorial process called "mutation". In this talk I will explain this connection, and describe a purely combinatorial approach to classifying Fano manifolds in any dimension.