Tropical surgeries in moduli theory and applications

Dhruv Ranganathan (Cambridge)

Monday 10th June 16:00-17:00 Maths 311B

Abstract

The moduli space of tropical curves is a parameter space for certain metric graphs, and enjoys an analogous relationship with the moduli space of curves as a fan does with its associated toric variety. By performing surgeries to this tropical moduli space, one obtains a series of birational models of the moduli space of curves, each of which is a moduli space in its own right. After explaining this idea, I will outline some applications. One of these applications contributes to our understanding of cycles in the moduli space of curves, and specifically to “toric contact cycles”, which generalize the double ramification cycle. 

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