I am broadly interested in algebraic geometry and combinatorics. Recently I have focused on moduli spaces arising in enumerative geometry. I have been using symmetric function theory, graph enumeration, and combinatorial topology to study certain aspects of the geometry and topology of these moduli spaces. Some of these techniques are related to tropical and logarithmic geometry. I have also become interested in applications of algebraic geometry to the study of matroids.
Preprints
Graph enumeration for moduli spaces of curves and maps, with Terry Dekun Song, submitted.
The S_n-equivariant Chow polynomial of the braid matroid, with Lukas Kühne, submitted.
Representation stability for moduli spaces of admissible covers, with Megan Chang-Lee and Philip Tosteson, submitted.
The S_n-equivariant Euler characteristic of \bar{M}_{1,n}(P^r,d), with Terry Dekun Song, submitted.
The dual complex of M_{1,n}(P^r,d) via the geometry of the Vakil--Zinger moduli space, with Terry Dekun Song, submitted.
Publications
On the weight zero compactly supported cohomology of H_{g,n}, with Madeline Brandt and Melody Chan, in Forum Math. Sigma
Equivariant Hodge polynomials of heavy/light moduli spaces, with Stefano Serpente and Claudia 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 Sam Freedman and Joseph Hlavinka, in Port. Math.
Topology of tropical moduli spaces of weighted stable curves in higher genus, with Shiyue Li, Stefano Serpente, and Claudia 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 Dagan Karp and Shiyue Li, in J. Combin. Theory Ser. A
Frobenius distributions of elliptic curves in short intervals on average, with Anthony Agwu, Phillip Harris, Kevin James, and Huixi Li, in Ramanujan J.
Frobenius distributions in short intervals for CM elliptic curves, with Anthony Agwu, Phillip Harris, Kevin James, and Huixi Li, in J. Number Theory
On consecutive primitive nth roots of unity modulo q, with Thomas Brazelton, Joshua Harrington, and Matthew Litman, in J. Number Theory
Expository
an informal introduction to blow-ups (warning: confusion of normal and conormal bundle)