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The topology of moduli spaces

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If you have a question about this talk, please contact Alexis Marchand.

The homology of moduli spaces of curves has long been studied and exhibits hidden structures of characteristic classes of families of curves. However, until very recently understanding non-tautological homology was not understood with few examples. I will explain some recent work of Chan-Galatius-Payne which allows computations of the pieces of the weight filtration on the cohomology with methods from tropical and logarithmic geometry. I will also explain some further routes of study to the homology of other moduli spaces, such as moduli spaces of stable maps.

This talk is part of the Junior Geometry Seminar series.

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