Research overview

I work in arithmetic geometry, a field that leverages the tools developed in algebraic geometry to gain deep insights into number theory. Specifically, I am interested in the geometry of characteristic-p Shimura varieties, and how number theorists apply them to other structures. Recently, I have been focusing on the moduli space of abelian varieties with certain extra structures, which constitute a popular class of Shimura varieties. Here is a more detailed Research Statement.

During my M.S. at the University of Michigan, I did some work in commutative algebra and finite geometry. Before that, my undergraduate research was in theoretical physics.


Publications and Preprints

Arithmetic geometry:

This paper concerns the characteristic-p fibers of GU(q-2,2) Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort stratification, based on the isomorphism class of the p-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the p-divisible group. It is natural to ask which Ekedahl-Oort strata intersect the unique closed Newton stratum, called the supersingular locus. In this paper, we present several novel techniques that give information about the interaction between the two stratifications for general signature (q-2,2), and as an application, we completely answer this question for the signature (3,2). 


This is joint work with Deewang Bhamidipati, Maria (Mia) Fox, Steven Groen, Heidi Goodson, and Emerald Anne. This preprint was a result of RNT - 3.  We benefitted from an AIM SQuaRe to wrap up this project and begin the next one. 


Commutative algebra:

The cancellation problem asks whether A[X_1, X_2, . . . , X_n] ≅ B[Y_1, Y_2, . . . , Y_n] =>A ≅ B. Hamann introduced the class of steadfast rings as the rings for which a version of the cancellation problem considered by Abhyankar, Eakin, and Heinzer holds. By the work of Asanuma, Hamann, and Swan, steadfastness can be characterized in terms of p-seminormality, which is a variant of normality introduced by Swan. We prove that p-seminormality and steadfastness deform for reduced Noetherian local rings. We also prove that p-seminormality and steadfastness are stable under adjoining formal power series variables for reduced (not necessarily Noetherian) rings. Our methods also give new proofs of the facts that normality and weak normality deform, which are of independent interest. 

This is joint work with Alexander Bauman, Havi Ellers, Gary Hu, Takumi Murayama, and Ying Wang.

This work was a result of MREG 2021.


In this paper, we study maximal sets of skew lines on Hermitian surfaces. We give a new algorithm to compute these sets and give some computational results for Hermitian surfaces of degrees 3, 4, and 5. In more generality, this algorithm solves a new variant of the clique listing problem, which may be more approachable than the classical problem. Finally, we explicitly construct a large skew set of lines on Hermitian varieties of any degree and use it to give a lower bound on the largest size of maximal skew sets and a lower bound on the possible number of maximal skew sets.

This is joint work with Anna Brosowsky, Haoyu Du, Madhav Krishna, Janet Page, and Tim Ryan.

This work was a result of LoG(M) 2022.

Other scholarly works

a. General treatment of Ekedahl-Oort and Newton stratification for PEL type unitary Shimura Varieties for unramified primes..

b. PEL type unitary Shimura Variety of signature (2,2) when the prime p is assumed to be unramified.

c. PEL type GU(n-1,1) Shimura Variety when the prime p is assumed to be unramified.

d. PEL type GU(n-1,1) Shimura Variety when the prime p is assumed to be ramified.