Counting Graphs on Surfaces

Abstract: We describe two problems arising from the general problem of counting special embeddings/immersions of graphs in surfaces, both of which can be turned into lattice point counting problems in an appropriate space, bringing together ideas from geometry, dynamics, and number theory. The first part of the talk is joint work with David Aulicino and Harry Richman, and the second part of the talk is joint work with Tarik Aougab.