Seminar in Real and Complex Geometry
Thursday, February 1, 2024, 16:15-17:45,
online via zoom
Renzo Cavalieri
(Colorado State University)
A log/tropical take on Hurwitz numbers
Abstract
I will present some joint work with Hannah Markwig and Dhruv Ranganathan, in which we
interpret double Hurwitz numbers as intersection numbers of the double ramification
cycle with a logarithmic boundary class on the moduli space of curves. This approach
removes the "need" for a branch morphism and therefore allows the generalization to
related enumerative problems on moduli spaces of pluricanonical divisors - which have
a natural combinatorial structure coming from their tropical interpretation. I will
discuss some generalizations springing out from this approach that are currently being
pursued in joint work with Hannah Markwig and Johannes Schmitt.
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