Shiyue (詩樂) Li

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

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

Prior to Brown, I studied math at Yale University and had spent wonderful four years of undergrad at Harvey Mudd College doing math and music. My undergrad thesis work was advised by Dagan Karp.

I also enjoyed computing and AI, while working at Google Research.

Here are my CV, GitHub, Google Scholar, and Email.

Research

Papers

  • Relative Bott-Samelson varieties
    (arxiv 2011.04814)
    We prove that, defined with respect to versal flags, the product of two relative Bott-Samelson varieties over the flag bundle is a resolution of singularities of a relative Richardson variety. This result generalizes Brion's resolution of singularities of Richardson varieties to the relative setting. It reflects the phenomenon that the local geometry of a relative Richardson variety is completely governed by the two intersecting relative Schubert varieties, studied by Chan-Pflueger. We also prove an analogous theorem in the case of relative Grassmannian Richardson varieties, thereby furnishing a resolution of singularities for the Brill-Noether variety with imposed ramification on twice-marked elliptic curves.

  • Topology of tropical moduli space of weighted stable curves in higher genus
    (arxiv 2010.11767, with Siddarth Kannan, Stefano Serpente, Claudia Yun)
    We show that the moduli spaces of weighted stable tropical curves of volume one are simply-connected for all genus greater than zero and all rational weights, under the framework of symmetric Delta-complexes and via a result by Allcock-Corey-Payne 19. We also calculate the Euler characteristics of these spaces and the top weight Euler characteristics of the classical Hassett spaces by exhibiting a useful decomposition of the class of the classical Hassett spaces in the Grothendieck group of varieties.

  • 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
    Heavy/light Hassett spaces are moduli space of rational curves with weighted marked points that satisfy a “heavy/light” and a stability condition. We present a computation of the Chow ring of such spaces via tropical geometry. Our computation weaves together many beautiful combinatorial gadgets that appear in algebraic geometry. The starting point of our computation is to view these spaces as tropical compactifications of hyperplane arrangement complements, using work by Cavalieri-Hampe-Markwig-Ranganathan. Then the computation of the Chow ring then reduces to intersection theory on the toric variety of the Bergman fan of a graphic matroid. In particular, this reduction allows us to bijectively correspond divisors of the related toric variety to trees with stable weighted rays, thereby computing the final Chow ring combinatorially.

In Preparation

  • Moduli space of curves with cyclic action
    with Emily Clader, Chiara Damiolini, Daoji Huang, Rohini Ramadas.
  • Topological zeta functions of matroids
    with Max Kutler, Dawit Mengesha, Robert Miranda, Brian Sun.

Undergrad Senior Thesis

Teaching

Canada/USA Mathcamp

Misc