Tropical Psi Classes and Tropicalizations of Psi Classes

Explore a 51-minute lecture from the Workshop on Combinatorics of Enumerative Geometry where Renzo Cavalieri from Colorado State University delves into the complex relationship between tropical geometry and moduli spaces, focusing specifically on psi classes. Learn how tropical psi classes, first introduced by Mikhalkin in the early 2000s, work seamlessly in genus zero but present significant challenges in higher genus. Discover the groundbreaking work by Kerber-Markwig and Katz that demonstrated the alignment of tropical and algebraic psi class intersection numbers. Examine the 2021 research conducted by Cavalieri, A.Gross, and H.Markwig that tackled tropical psi classes in higher genus by transforming the tropical moduli space of curves into a stack for families of tropical curves with an affine structure. Understand their combinatorial theory that not only recovers algebraic intersection numbers but also yields unique results without algebraic geometry counterparts. Follow the recent developments with A.Gross in determining when tropical psi classes can be considered tropicalizations, including their innovative approach to tropicalization for curve families based on base Picard theory.