Geometry Seminar

A closed surface can be endowed with a certain locally Euclidean metric structure called a translation surface. Moduli spaces that parametrize such structures are called strata, and there is still much to discover of their global topology. These strata admit a decomposition into finitely many polytopal regions parametrized by certain triangulations of translation surfaces (L-infinity Delaunay triangulations). These regions are adjacent to each other in pathological ways, but it was conjectured by Frankel that these pathologies can be nicely classified. We affirm this conjecture of Frankel, and use the resulting classification to give an explicit presentation of strata as quotients of locally finite simplicial complexes via the action of the mapping class group. Speaker(s): Bradley Zykoski (Michigan)