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.