Voronoi Cells, Zonotopes, and Tropical Algebraic Curves

Wednesday, April 30, 2025

3:00 PM-4:30 PM

Speaker: Yelena Mandelshtam, Institute for Advanced Studies, Princeton

Voronoi cells and Delaunay subdivisions show up in all sorts of places—from modeling crystal structures to studying lattices and solving optimization problems. In this talk, I’ll introduce these geometric objects and explain how they’re connected to zonotopes, a special class of polytopes built from line segments, and to the theory of matroids, which capture combinatorial notions of dependence. These ideas also play a role in more recent developments in tropical geometry, where classical tools from algebraic geometry take on a piecewise-linear form. I’ll give an overview of how this framework leads to the tropical Schottky problem, which asks which tropical abelian varieties come from algebraic curves.