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Sam Payne, Zoom: Tropical curves, graph complexes, and top weight cohomology of M_g
Thursday, September 03, 2020, 03:30pm - 04:30pm
The cohomology of the moduli space of curves is an object of central interest in algebraic geometry, topology, and mathematical physics. I will discuss one part of this cohomology (the top graded piece of the weight filtration) that is essentially combinatorial. This top weight cohomology is naturally identified with the reduced homology of a moduli space of stable tropical curves, and with the homology of Kontsevich's graph complex. As an application, we show that H^{4g-6}(M_g) is nonvanishing for large g, refuting conjectures of Kontsevich and of Church, Farb, and Putman, and even grows exponentially. Joint work with M. Chan and S. Galatius.
Location: Zoom

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