Research

My areas of interest are in arithmetic statistics and arithmetic geometry. More specifically, I like to count points on various schemes/stacks, looking at p-adic densities/integrals, and looking at asymptotics in p (such as looking at statistics of numerical invariants of varieties mod p as p grows). I am also interested in the application of logic to number theory, and applications of number theory/algebraic geometry to computer algorithms. 

Papers and preprints (in reverse chronological order):

1. Counting Rational Points on the Stacky Sym^2 P^1. (2023) arxiv.org/abs/2309.14549 

2. A Chebotarev Density Theorem over Local Fields. With Asvin G, Yifan Wei. (2022) arxiv.org/abs/2212.00294 

3. Density of p-adic polynomials generating extensions with fixed splitting type. (2022) arxiv.org/abs/2211.10425 GitHub link as mentioned in the paper 

4. On an algorithm converging to hyperstochastic tensors. (2022) With Will Hardt. Link 

5. Linear Relations Among Galois Conjugates Over Fq(t). (2022) With Will Hardt. arxiv.org/abs/2103.10612 

6. Empirical properties of optima in free semidefinite programs. (2023) With Eric Evert, Yi Fu, John William Helton. arxiv.org/pdf/2006.02248.pdf 

7. ASTRAL-MP: scaling ASTRAL to very large datasets using randomization and parallelization. With Chao Zhang, Siavash Mirarab.
   Bioinformatics, Volume 35, Issue 20, 15 October 2019, Pages 3961–3969, https://doi.org/10.1093/bioinformatics/btz211

Notes/slides of talks:

1. Poster presentation on counting points on stacky Sym^2(P^1) poster 

2. UW Madison Graduate Number Theory talk on Heights on Stacks slides

3. UW Madison Graduate Number Theory talk on Bertini Theorem over Finite Fields slides

Some GitHub links:

1. Sagemath code referenced in my paper on the Density of p-adic polynomials generating extensions with fixed splitting type. Link