Frankfurter Seminar – Kolloquium des Instituts für Mathematik

Renzo Cavalieri (Colorado State University, Fort Collins)

Abstract: Enumerative geometry is an ancient branch of mathematics that aims to count the number of geometric objects that satisfy some constrains: the primordial enumerative geometric statement is that there is a unique straight line that passes through two distinct points in a plane. While enumerative geometric questions are often easy to state, the attempts to answer them have both employed and spurred the development of several mathematical techniques.
This talk will be a broad and hopefully friendly survey of how tropical geometry has become an important actor for several enumerative problems especially related to counting curves. I will use Hurwitz theory as the running example, and show how tropical geometry provides us not only with an interesting approach to classical Hurwitz theory, but also allows us to define „new“ enumerative problems of Hurwitz type. Much of the work presented has been collaborative work with Paul Johnson, Hannah Markwig, Dhruv Ranganathan and Johannes Schmitt.