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Geometry of the double ramification cycle

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If you have a question about this talk, please contact Dhruv Ranganathan.

The double ramification cycle on the moduli space of curves measures how often a `random’ divisor on a curve is principal. We will begin by recalling the basic construction, and explaining how to extend this to the boundary of the moduli space (the latter was for some time an open problem, but now has several equivalent solutions). We will then look deeper into the geometric properties of this cycle, in particular its self-intersection, with the aim of explaining why the double ramification cycle should really be seen as living in the (as-yet undefined) logarithmic Chow ring. Parts of this story are joint work with Jesse Kass, Nicola Pagani, Aaron Pixton and Johannes Schmitt.

This talk is part of the Algebraic Geometry Seminar series.

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