Shiyue Li 詩樂

I’m a PhD student in Mathematics at Brown University. I’m fortunate to be advised by Melody Chan.

My research interests sit in the intersection of algebraic geometry, combinatorics and topology. More specifically, I think about matroids, Schubert calculus, enumerative geometry, moduli spaces of curves and their combinatorics induced by tropical geometry.

Prior to Brown, I was at Yale University and Harvey Mudd College, doing math and (an excessive amount of) music. My undergrad thesis work was advised by Dagan Karp.

I also enjoy computing and AI, and worked at Google Research.

Here are my CV, Google Scholar, and Email.

Research

Papers

  1. Permutohedral complexes and rational curves with cyclic action
    (arxiv 2104.06526, with Emily Clader, Chiara Damiolini, Daoji Huang, Rohini Ramadas)
    We construct a moduli space of rational curves with finite-order automorphism and weighted orbits, and studied a three-way bijection between the boundary strata of the moduli space, the faces of a polytopal complex, and certain cosets of the complex reflection group.

  2. Relative Bott-Samelson varieties
    (arxiv 2011.04814)
    We generalize Brion's Bott-Samelson resolution of singularities of Richardson varieties to a relative setting. We then applied it to give a resolution of singularities for the Brill-Noether variety with imposed ramification on twice-marked elliptic curves, studied by Chan-Pflueger-Osserman.

  3. Topology of tropical moduli space of weighted stable curves in higher genus
    (arxiv 2010.11767, with Siddarth Kannan, Stefano Serpente, Claudia Yun; slides)
    We prove the simple connectivity of the moduli spaces of weighted stable tropical curves of volume one, for all higher genus and all rational weights. We also compute their Euler characteristics.

  4. Chow ring of heavy/light Hassett spaces via tropical geometry
    (arxiv 1910.10883, with Siddarth Kannan and Dagan Karp)
    Journal of Combinatorial Theory, Series A. 178C (2021) 105348
    We compute the Chow ring of heavy/light Hassett spaces of genus zero via tropical compactification and toric intersection theory.

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