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Presented By: Department of Mathematics

Colloquium Series Seminar

Tropical curves, graph homology, and top weight cohomology of M_g

I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of M_g and also with the homology of Kontsevich's graph complex. As one application, we show that H^{4g-6}(M_g) grows exponentially with g. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. As another application, we prove a formula conjectured by Zagier for the S_n-equivariant top weight Euler characteristic of M_{g,n}.

Based on joint work with M. Chan, C. Faber, and S. Galatius. Speaker(s): Sam Payne (University of Texas at Austin)

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