Moduli spaces of tropical curves and tropical psi classes

Algebra Seminar
Tuesday, September 28, 2021 - 10:00am for 1 hour (actually 50 minutes)
Skiles 006
Andreas Gross – Georgia Tech –
Ashley K. Wheeler

Tropical curves are piecewise linear objects arising as degenerations of algebraic curves. The close connection between algebraic curves and their tropical limits persists when considering moduli. This exhibits certain spaces of tropical curves as the tropicalizations of the moduli spaces of stable curves. It is, however, still unclear which properties of the algebraic moduli spaces of curves are reflected in their tropical counterparts. In my talk, I will report on joint work with Renzo Cavalieri and Hannah Markwig, in which we define tropical psi classes and study relations between them. I will explain how some of the expected identities cannot be recovered from a purely tropical perspective, whereas others can, revealing the tropical nature they have been of in the first place.