Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 3

Explore the third 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 and their interpretation as intersection numbers of double ramification cycles with elements of the log Chow ring. Examine recent advancements in associating piecewise polynomial functions to k-DR cycles, leading to k-analogues of Hurwitz numbers called leaky Hurwitz numbers. Discover ongoing research incorporating descendants into these concepts, including tropical algorithms yielding simple formulas for fully ramified points. Gain insights from years of collaborative work with experts in the field during this hour-long presentation from the Workshop on "Non-commutative Geometry meets Topological Recursion" at the Erwin Schrödinger International Institute for Mathematics and Physics.