Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 1

Explore the intersection of tropical geometry and enumerative geometry in this lecture from the Workshop on "Non-commutative Geometry meets Topological Recursion" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the development of tropical Hurwitz numbers as combinatorial analogues for classical Hurwitz numbers, and examine their interpretation as intersection numbers of double ramification cycles with elements of the log Chow ring. Discover how tropical perspectives give rise to k-analogues of Hurwitz numbers, known as leaky Hurwitz numbers, and their algebraic and combinatorial properties. Learn about ongoing research incorporating descendants into these frameworks, including tropical algorithms yielding simple formulas for fully ramified points. Gain insights from years of collaborative work in this field, presented by Renzo Cavalieri with assistance from Carlos I. Pérez Sánchez.