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 some special manifolds admitting a torus symmetry. The latter is encoded in a map, called moment map, which "transforms" the 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 the class of reflexive polytopes, which was introduced by Batyrev in the context of mirror symmetry, and explain how the "12" and "24" phenomenon for reflexive polytopes of dimensions 2 and 3 can be generalized to higher dimensions using symplectic geometry.
Donnerstag, den 7. Februar 2019 um 17.15 Uhr, in INF 205, HS Mathematikon Donnerstag, den 7. Februar 2019 at 17.15, in INF 205, HS Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers