Photo of Shiyue Li
Photo credit: my friend, Haoxing Du

Shiyue Li 李詩樂

Donald J. Lewis Assistant Professor (non-tenure-track)
Department of Mathematics, University of Michigan

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 and Federico Ardila-Mantilla.

In 2023, I received my PhD in mathematics from Brown University, where I was fortunate to be advised by Melody Chan.

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

I am on the job market for academic positions, or research positions concerning AI safety and alignment (for humanity in general or for mathematics), starting in 2027.

Research

  1. Chow polynomials and chain polynomials of matroids are not log-concave

    with Gergely Bérczi, Basile Coron, and Chris Eur

    arXiv:2610.17135

    Abstract

    We construct explicit counterexamples from finite geometries to log-concavity of Chow polynomials, chain polynomials, and augmented Chow polynomials of matroids, disproving real-rootedness conjectures of Huh–Stevens, Ferroni–Schröter, and Athanasiadis–Kalampogia-Evangelinou from the lowest possible ranks.

  2. Magic positivity of Snapper polynomials for matroids

    arXiv:2609.24917

    Abstract

    Snapper polynomials are Euler characteristics of tensor powers of line bundles on a normal complete algebraic scheme. Positivity properties of line bundles can be phrased using positivity of Snapper polynomials. We investigate their magic positivity and real-rootedness. We introduce zonotopal classes in the Grothendieck KK-ring of vector bundles of the toric variety for any loopless matroid, and analogous classes on the Deligne–Mumford–Knudsen compactification of stable pointed curves. We prove that their Snapper polynomials are magic positive, so their coefficients are nonnegative and their h∗h^*-polynomials are real-rooted. For cotangent line bundles whose first Chern classes are distinct ψ\psi-classes, which are not zonotopal, we nonetheless prove that their h∗h^*-polynomials are real-rooted, whereas their Snapper polynomials are magic positive if and only if n⩽7n \leqslant 7. More generally, we introduce saturated and weakly saturated KK-classes of matroids, which furnish a sufficient and a necessary condition for magic positivity of Snapper polynomials in terms of their dragon Hall–Rado polymatroids.

  3. Matroid analogues of Gal’s conjecture

    with Basile Coron and Luis Ferroni

    arXiv:2604.04550

    Abstract

    We formulate and prove matroid analogues of the Charney–Davis, Gal, and Nevo–Petersen conjectures in the setting of Chow polynomials of matroids with flag and complete building sets, which we introduce. Our proofs analyze the underlying toric varieties and show that the toric varieties undergo geometric changes that preserve γ\gamma-positivity, as one varies the building set to achieve complete and flag building sets. In the complete case, we construct a simplicial complex whose ff-vector is the γ\gamma-vector. We also obtain a new combinatorial formula for the γ\gamma-expansion of the Poincaré polynomial of the Deligne–Mumford–Knudsen moduli space of rational stable marked curves.

  4. Structural properties of nested set complexes

    with Basile Coron and Luis Ferroni

    arXiv:2601.05188

    Abstract

    We prove that nested set complexes are vertex decomposable and admit convex ear decompositions. As an application, we prove that the hh-vector is strongly flawless, and in particular, top-heavy. We specialize to the boundary complex of the Deligne–Mumford–Knudsen compactification of rational stable marked curves to derive new decompositions and new formulas for its hh-vector.

  5. Chow polynomials of rank-uniform labeled posets

    with Basile Coron and Luis Ferroni

    arXiv:2511.13819

    Abstract

    We introduce the notion of UMEL-shellable posets. They are posets admitting an edge-lexicographic labeling with certain uniformity and monotonicity conditions. These include uniform matroids, projective and affine geometries, Dowling geometries (including braid matroids of types 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.

  6. Kapranov degrees

    with Joshua Brakensiek, Chris Eur, and Matt Larson

    International Mathematics Research Notices (2025) arXiv:2308.12285

    Abstract

    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 ψ\psi-classes. This framework unifies intersection numbers computed by Witten, Silversmith, Castravet-Tevelev, Postnikov, Cavalieri-Gillespie-Monin, and Gillespie-Griffin-Levinson. We prove a positivity characterization and an upper bound, using matroid theory and the theory of error correcting codes.

  7. Multimatroids and rational curves with cyclic action

    with Emily Clader, Chiara Damiolini, Chris Eur, and Daoji Huang

    International Mathematics Research Notices (2024) arXiv:2311.09314 Video

    Abstract

    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-AA permutohedral varieties (Losev–Manin moduli spaces) and matroids, and the connection between type-BB 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 divisors are Lorentzian.

  8. Equivariant log-concavity of independence sequences of claw-free graphs

    Séminaire Lotharingien de Combinatoire 89B (2023)

    Abstract

    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 of Hamidoune and of Chudnovsky–Seymour.

  9. KK-rings of wonderful varieties and matroids

    with Matt Larson, Sam Payne, and Nick Proudfoot

    Advances in Mathematics 441 (2024) arXiv:2210.03169 Video

    Abstract

    We study the KK-rings of wonderful compactifications of hyperplane arrangement complements and of arbitrary matroids. We prove a Hirzebruch–Riemann–Roch-type formula, and an isomorphism between the integral KK-rings and the Chow rings that replaces the Chern character. We introduce Euler characteristics of vector bundles on arbitrary matroids as matroid invariants. We apply these tools to Deligne–Mumford–Knudsen moduli spaces of stable rational curves with marked points.

  10. Wonderful compactifications and rational curves with cyclic action

    with Emily Clader, Chiara Damiolini, and Rohini Ramadas

    Forum of Mathematics, Sigma 11 (2023) arXiv:2208.05463

    Abstract

    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.

  11. Equivariant log-concavity of graph matchings

    Algebraic Combinatorics 6 (2023) arXiv:2202.08828

    Abstract

    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.

  12. Relative Bott–Samelson varieties

    La Matematica 2 (2023) arXiv:2011.04814

    Abstract

    We construct relative Bott–Samelson resolutions of singularities of Richardson varieties. We then apply them to give a resolution of singularities for the Brill-Noether variety with imposed ramification on twice-marked elliptic curves, studied by Chan–Osserman–Pflueger.

  13. Topology of tropical moduli spaces of weighted stable curves in higher genus

    with Siddarth Kannan, Stefano Serpente, and Claudia He Yun

    Advances in Geometry 23(3) (2023) arXiv:2010.11767 Slides

    Abstract

    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.

  14. Permutohedral complexes and rational curves with cyclic action

    with Emily Clader, Chiara Damiolini, Daoji Huang, and Rohini Ramadas

    manuscripta mathematica (2022) arXiv:2104.06526

    Abstract

    We construct a moduli space of rational curves with finite-order automorphism and weighted orbits, and study 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.

  15. Intersecting psi-classes on tropical Hassett spaces

    with Marvin Anas Hahn

    Combinatorial Theory, 2(3) (2022) arXiv:2108.00875

    Abstract

    We compute the intersection numbers of tropical ψ\psi-classes on tropical heavy/light Hassett spaces, generalizing a result of Kerber–Markwig.

  16. Chow ring of heavy/light Hassett spaces via tropical geometry

    with Siddarth Kannan and Dagan Karp

    Journal of Combinatorial Theory, Series A. 178C (2021) arXiv:1910.10883

    Abstract

    We compute the Chow ring of heavy/light Hassett spaces of genus zero via tropical compactification and toric intersection theory.

Invited talks

Lecture notes

University of Michigan

Canada/USA Mathcamp

I felt at home and had tons of fun at Mathcamp 2018 and 2019. See below for notes of classes I taught.

Music & Mountains

I am an avid amateur musician. I have played the piano since I was four and the classical guitar since I was twelve, and I especially love playing Bach on both. Lately I have been working on the Goldberg Variations and the Chaconne from Bach’s Partita No. 2. I also enjoy thinking and chatting about music theory, composition, and ethnomusicology. I spend a lot of time exploring all sorts of music: jazz, world, indie, alternative, experimental, weird genres, etc. Feel free to exchange listening lists with me!

In my spare time, I like to trail run, and I try to run a half marathon race every year. I also love being in the high-altitude mountains and have summited several peaks above 4,000 m in the lower 48 states. A place that’s very special to me is Chamonix-Mont-Blanc in the French Alps. Sadly, its glaciers are in a devastating state, which makes my heart ache: the heat wave has brought severe melt on the Argentière and Bossons glaciers. I hope we act before it’s too late.

Climber on a snowy ridge of the Aiguilles d'Entrèves
Traversing the border of France and Italy on the Aiguilles d'Entrèves (3,600 m).