About
I'm an enumerative algebraic geometer. My recent work has focused on the double ramification cycle, Gromov-Witten theory, and cohomological field theories. I am generally interested in problems dealing with intersection-theoretic classes on the moduli space of curves or related moduli spaces. Many enumerative questions (counting geometric objects with certain properties) can be reduced to computations involving such cycle classes, and many cycle classes appearing in geometry have beautiful explicit formulas as sums over isomorphism classes of decorated graphs.
Papers
Assorted research-related things
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Notes (2023) on the proof of the polynomiality of the double ramification cycle (following Zagier).
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My lecture on the double ramification cycle at the 2022 ICM, along with my contribution to the proceedings of the ICM.
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Videos from a series of lectures I gave on tautological rings of moduli spaces of curves at a summer school in Trieste (ICTP) in 2016: 1
2
3
4
5.
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My PhD thesis (2013) on the tautological ring, along with my senior thesis (2008) on Gromov-Witten invariants of elliptic curves (both advised by Rahul Pandharipande).
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I contributed some of the original code for the SageMath module admcycles for explicit computations in the tautological ring of the moduli space of curves, and I highly recommend it for anyone computing things involving tautological classes.
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Some ranks of S_n-invariant parts of tautological rings I computed in 2013: stable curves, compact type, powers of the universal curve. (Nowadays admcycles can compute these and much more!)
Teaching
Students
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Current: Michael Mueller, Qiusheng Zhao.
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Former: Nawaz Sultani (2022, co-advised with Felix Janda and Yongbin Ruan), Rachel Webb (2020, co-advised with Yongbin Ruan).
