Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 2

Explore the second lecture in a series on tropical geometry's contributions to enumerative geometry, focusing on target dimension one. Delve into the development of tropical Hurwitz numbers as combinatorial analogues for classical Hurwitz numbers. Examine the interpretation of tropical Hurwitz numbers as intersection numbers of double ramification cycles with elements of the log Chow ring. Investigate the concept of branch polynomials and their relation to tropical moduli spaces of covers. Learn about k-DR cycles and their associated piecewise polynomial functions, leading to k-analogues of Hurwitz numbers called leaky Hurwitz numbers. Discover 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 at the Workshop on "Non-commutative Geometry meets Topological Recursion" held at the Erwin Schrödinger International Institute for Mathematics and Physics.