In recent years I have been particularly interested in moduli spaces of curves and related objects. The geometry of these spaces is closely related to enumerative theories of curves, especially Gromov--Witten theory.
I generally like explicit calculations, and much of my recent work focuses on establishing formulas for motivic invariants of these moduli spaces. In addition to algebro-geometric techniques, combinatorial tools are quite powerful in this context: for example, I've used symmetric functions, graph theory, combinatorial topology, and tropical geometry to study these spaces.
I also think about graph complexes and operads from algebraic topology, as well as applications of algebraic geometry to the study of matroids.
Preprints
Motivic quasimap wall-crossing for Grassmannians, with T. Song.
Automorphisms of the boundary complex of \bar{M}_{0,n}(P^r, d), with A. Joisha.
Virtual Hodge numbers of M_{g,n}(P^r, d): stability and calculations, with T. Song.
Graph enumeration for moduli spaces of curves and maps, with T. Song. [extended abstract]
Publications
Euler characteristics of the universal Picard stack, to appear in Int. Math. Res. Not. IMRN.
The S_n-equivariant Chow polynomial of the braid matroid, with L. Kühne, to appear in Épijournal Géom. Algébrique.
Representation stability for moduli spaces of admissible covers, with M. Chang-Lee and P. Tosteson, to appear in Int. Math Res. Not. IMRN.
The S_n-equivariant Euler characteristic of \bar{M}_{1,n}(P^r,d), with T. Song, in J. Reine Angew. Math. [code]
The dual complex of M_{1,n}(P^r,d) via the geometry of the Vakil--Zinger moduli space, with T. Song, in Adv. Math.
On the weight zero compactly supported cohomology of H_{g,n}, with M. Brandt and M. Chan, in Forum Math. Sigma
Equivariant Hodge polynomials of heavy/light moduli spaces, with S. Serpente and C. Yun, in Forum Math. Sigma [code]
Moduli of relative stable maps to P^1: cut-and-paste invariants, in Sel. Math. New Ser. [video, slides]
Automorphisms of tropical Hassett spaces, with S. Freedman and J. Hlavinka, in Port. Math.
Topology of tropical moduli spaces of weighted stable curves in higher genus, with S. Li, S. Serpente, and C. Yun, in Adv. Geom.
Symmetries of tropical moduli spaces of curves, in Trans. Amer. Math. Soc.
Chow rings of heavy/light Hassett spaces via tropical geometry, with D. Karp and S. Li, in J. Combin. Theory Ser. A
Frobenius distributions of elliptic curves in short intervals on average, with A. Agwu, P. Harris, K. James, and H. Li, in Ramanujan J.
Frobenius distributions in short intervals for CM elliptic curves, with A. Agwu, P. Harris, K. James, and H. Li, in J. Number Theory
On consecutive primitive nth roots of unity modulo q, with T. Brazelton, J. Harrington, and M. Litman, in J. Number Theory
Other writing
Pólya enumeration, wreath product symmetric functions, and moduli spaces of curves (extended abstract accepted to FPSAC 2026)
an informal introduction to blow-ups (warning: confusion of normal and conormal bundle)
Co-authors
Anthony Agwu, Madeline Brandt, Thomas Brazelton, Melody Chan, Megan Chang-Lee, Sam Freedman, Joshua Harrington, Phillip Harris, Josie Hlavinka, Kevin James, Arjun Joisha, Dagan Karp, Lukas Kühne, Huixi Li, Shiyue Li, Matthew Litman, Stefano Serpente, Terry Dekun Song, Philip Tosteson, Claudia Yun