Research

I am mainly interested in number theory and arithmetic statistics, particularly questions related to elliptic curves, Selmer groups, and counting number fields. I am also interested in prime number races, special values of L-functions, effective estimates, and some related topics in combinatorics.

The following are my papers and preprints.  I have linked to journal versions where possible; preprints of all of papers can be found on arXiv. 

Published:

1. Comparing the Density of D4  and S4 Extensions of Number Fields, with Matt Friedrichsen 

Proceedings of the American Mathematical Society | 2021 | pdf | slides | journal 

2. Enumerating  D4  Quartics and a Galois Group Bias Over Function Fields 

Journal de Théorie des Nombres de Bordeaux | 2022 | pdf | slides | journal 

3. Mertens' Theorem for Chebotarev Sets, with Santiago Arango-Piñeros and Chris Keyes 

International Journal of Number Theory | 2022 | pdf | journal 

4. Optimal Transport for Some Symmetric Multidimensional Partitions, with Daniel Adu 

Discrete Applied Mathematics | 2023 | pdf | journal

5. Exceptional Biases in Counting Primes Over Function Fields, with Alexandre Bailleul, Lucile Devin and Wanlin Li

Journal of the London Mathematical Society | 2024 | pdf | journal | slides

6. On the constants in Mertens' theorems for primes in arithmetic progressions, with Ethan S. Lee 

Proceedings of the Integers Conference 2023  | 2024 | pdf | journal 

Preprints:

7.  Rank Growth of Elliptic Curves in S4  and A4  Extensions of the Rationals 

Submitted | 2022 | pdf | slides 

8. Dominant Galois Groups for Large Degree Extensions, with Jiuya Wang

In preparation | slides 

I have also worked in computational genomics. The papers and abstracts below are the result of collaboration with Eli Van Allen, David Liu, and others at the Dana-Farber Cancer Insitute. My contributions primarily dealt with applications of non-negative matrix factorization to problems about mutational signatures. Check out related work from the Van Allen Lab. Though this is not my current research focus, I am very interested in revisiting some of these ideas with topological methods. Research from this work can be found at PubMed or on Google Scholar.  Here are the highlights: 

1. Mutational patterns in chemotherapy resistant muscle-invasive bladder cancer,  D. Liu, P. Abbosh, D. Keliher, et al.

Nature Communications | 2017 | journal 

2. Genomic correlates of response to immune checkpoint blockade in microsatellite-stable solid tumors, D. Miao, P. Rescigno, D. Liu, et al. 

Nature Genetics  | 2018 | journal 

3. Immunogenomic analyses associate immunological alterations with mismatch repair defects in prostate cancer,  D.N. Rodrigues, P. Rescigno, D. Liu, et al.

The Journal of Clinical Oncology | 2019 | journal

4. Clinical interpretation of integrative molecular profiles to guide precision cancer medicine, B. Reardon, N. D. Moore, N. Moore, et al. 

Nature Cancer | 2021 | journal

Other Stuff

In December 2023, Jiuya Wang and I hosted a number theory conference, PANTS XXXVII, at UGA. 

For many years I organized the Tufts University Directed Reading Program (DRP). In Fall 2022, I participated in the Spelman-Morehouse DRP. 

From Spring 2019 to Fall 2021, I organized  the Tufts Math Graduate Student Seminar, which is now run by J.C. Wang.