Speaker: Renzo Cavalieri (Colorado State)

Title: Tropicalizing a Hurwitz theorist

Abstract: The goal is to review and contextualize the evolution of my thoughts and interactions with tropical geometry. This talk is based on collaborative work always with Hannah Markwig, and at different times with each one of Aaron Bertram, Paul Johnson and Dhruv Ranganathan.
Back in 2007, Hannah Markwig approached me after being told by Paul Johnson that covers smelled like cut and join. Deciphering Paul's oracle was the beginning of a fruitful and ongoing collaboration, that is pulling me closer and closer to the tropical world.
Over the course of the years, we have been studying Hurwitz theory and Gromov-Witten theory, first using tropical geometry as a powerful combinatorial tool, and then trying to understand what is the conceptual reason for the remarkably tight connection between the boundary geometry of moduli spaces of curves and maps and the piecewise linear objects in tropical geometry. The introduction of the analytic point of view, brought to the moduli space of curves by Abramovich, Caporaso and Payne, offered not only a much sought for conceptual perspective, but also opened up the way for further investigation.