Shiyue Li 李詩樂

I am a Donald J. Lewis assistant professor at the University of Michigan, mentored by David Speyer.

I work in algebraic geometry and combinatorics. More specifically, I study combinatorial structures in algebraic varieties and their moduli spaces. I am broadly interested in questions connected to number theory, algebraic topology, and algebraic K-theory.

From 2023 to 2025, I was a member at the Institute for Advanced Study, mentored by June Huh.

In 2023, I got a PhD in mathematics at Brown University, where I was fortunate to be advised by Melody Chan.

Prior, I spent wonderful four years at Harvey Mudd College; my undergrad thesis work was guided by Dagan Karp.

Here are my Curriculum Vitae, Google Scholar, arXiv and Email.

Research

Papers

  1. Structural properties of nested set complexes
    (with Basile Coron, Luis Ferroni)
    We prove vertex decomposability and convex ear decompositions of nested set complexes. As an application, we prove that the h-vector is strongly flawless, and in particular, top-heavy. We specialize to the boundary complex of Deligne--Mumford--Knudsen compactification of rational stable marked curves to derive new decompositions and new formulas for its h-vector.

  2. Chow polynomials of rank-uniform labeled posets
    (with Basile Coron, Luis Ferroni)
    We introduce the notion of UMEL-shellable posets. They are posets admitting edge lexicographical labeling with certain uniformality and monotonicity conditions. These include uniform matroids, projective and affine geometries, Dowling geometries (including braid matroids of type A and B) and more generally rank-uniform supersolvable lattices. We prove that the Chow polynomials, the augmented Chow polynomials, and the chain polynomials associated with those posets only have real roots, thus making simultaneous progress towards conjectures by Ferroni–Schröter, Huh–Stevens, and Athanasiadis–Kalampogia-Evangelinou.

  3. Kapranov degrees
    (with Joshua Brakensiek, Christopher Eur, Matt Larson)
    International Mathematics Research Notices. (2025).
    We introduce the notion of Kapranov degrees. These are the multidegrees of the embedding of the Deligne--Mumford--Knudsen moduli space of rational stable curves with marked points into a product of projective spaces via the complete linear series of psi-classes. This framework unifies intersection numbers computed by Witten, Silversmith, Castravet-Tevelev, Postnikov, Cavalieri-Gillespie-Monin, and Gillespie-Griffins-Levinson. We prove a positivity characterization and an upper bound, using matroid theory and the theory of error correcting codes.

  4. Multimatroids and rational curves with cyclic action
    (with Emily Clader, Chiara Damiolini, Christopher Eur, Daoji Huang)
    International Mathematics Research Notices. (2024).
    We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids introduced by Bouchet, which naturally arise in topological graph theory. This framework generalizes the previous connection between type-A permutohedral varieties (Losev--Manin moduli spaces) and matroids, and the connection between type-B permutohedral varieties (Batyrev--Blume moduli spaces) and delta-matroids. We introduce and study nef divisors and independence polytopal complexes of multimatroids. We effectively prove that the volume polynomials of these diviors are Lorentzian.

  5. Equivariant log-concavity of independence sequences of claw-free graphs
    Séminaire Lotharingien de Combinatoire 89B. (2023).
    We prove that the graded permutation representation by independent vertex sets of any claw-free graph is strongly equivariantly log-concave. Our proof reduces the problem to the hard Lefschetz theorem on the cohomology of a product of projective lines. This gives a strengthening and a new proof of results by Hamidoune, and Chudnovsky--Seymour.

  6. K-rings of wonderful varieties and matroids
    (with Matt Larson, Sam Payne, Nick Proudfoot)
    Advances in Mathematics 441. (2024).
    We study the K-rings of wonderful compactifications of hyperplane arrangement complements and of arbitrary matroids. We prove a Hirzebruch--Riemann--Roch-type formula, an isomorphism between the integral K-rings and the Chow rings, replacing the Chern character. We introduce Euler characteristic of vector bundles of arbitrary matorids as matroid invariants. We apply these tools to Deligne--Mumford--Knudsen moduli spaces of stable rational curves with marked points.

  7. Wonderful compactifications and rational curves with cyclic action
    (with Emily Clader, Chiara Damiolini, Rohini Ramadas)
    Forum of Mathematics, Sigma 11. (2023).
    We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces. By proving a general result on such wonderful compactifications, we conclude that this moduli space is Chow-equivalent to an explicit toric variety (whose fan can be understood as a tropical version of the moduli space), from which a computation of its Chow ring follows.

  8. Equivariant log-concavity of graph matchings
    Algebraic Combinatorics 6. (2023) .
    We prove that the graded vector space spanned by matchings in any graph is strongly equivariantly log-concave, viewed as a graded permutation representation of the graph automorphism group. Our proof constructs equivariant injections by reducing to the hard Lefschetz theorem.

  9. Relative Bott--Samelson varieties
    La Matematica 2. (2023)
    We construct relative Bott--Samelson resolutions of singularities of Richardson varieties. 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--Osserman--Pflueger.

  10. Topology of tropical moduli space of weighted stable curves in higher genus
    (with Siddarth Kannan, Stefano Serpente, Claudia He Yun; slides)
    Advances in Geometry 23(3). (2023).
    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.

  11. Permutohedral complexes and rational curves with cyclic action
    (with Emily Clader, Chiara Damiolini, Daoji Huang, Rohini Ramadas)
    manuscripta mathematica. (2022)
    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.

  12. Intersecting psi-classes on tropical Hassett spaces
    (with Marvin Anas Hahn)
    Combinatorial Theory, 2(3). (2022).
    We compute the intersection numbers of tropical psi-classes on tropical heavy/light Hassett spaces, generalizing a result of Kerber--Markwig.

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

Invited talks

Teaching

Canada/USA Mathcamp

Music & Mountains

    I am an avid amateur musician and mountaineer.

    Piano

    My primary instrument is the piano, which I started playing at age 4. During college, I had a blast learning from Gayle Blankenburg, as well as from a group of extremely talented peers in her studio. I’ve been recently working on:

    • Bach - Goldberg Variations, BWV 988
    • Schubert - Fantasia in F-minor four 4 hands, D. 940
    • Beethoven – Spring Sonata for violin and piano

    Classical Guitar

    My secondary instrument is the classical guitar, also known as Spanish guitar, which I started learning at age 12. During college, I had fun studying guitar and baroque lute with Jack Sanders, and playing in the Pomona College Guitar Quartet from 2024 to 2016. I particularly love playing Bach's music on a guitar. I'm slowly working on:

    • Tárrega - Recuerdos de la alhamabra
    • Bach – Chaconne, Partita No. 2, BWV 1004

    Other Music

    I enjoy thinking and chatting about music theory, composition, and ethnomusicology. I have also sung in a cappella while at Yale.

    Alpine Climbs

    I can sometimes be found in the mountains.

    Mountain climbing
    Traversing the border of France and Italy on Aiguilles d'Entrèves (3600m).