Mathematische Gesellschaft

Donnerstag, 27.10.2016

Prof. Dr. Silvia Sabatini, Universtität Köln

A bridge from reflexive polytopes to symplectic geometry


Mathematics finds itself divided and subdivided into hyper-specialized areas of study, each of them with its own internal beauty. However, what I find most fascinating is when one can build a bridge between two of these seemingly isolated theories. For instance, symplectic geometry and combinatorics have a very strong connection, due to the existence of Hamiltonian torus actions. Such actions come with a map, called moment map, which ``transforms" a compact symplectic manifold into a convex polytope. Hence many combinatorial properties of (some special types of) polytopes can be studied using symplectic techniques. In this talk I will focus on reflexive polytopes of dimension 2 and 3, and explain the so called "12" and "24" phenomenon using symplectic geometry.