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 

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

(To Appear) Pacific Journal of Mathematics | 2024 | pdf | slides 

Preprints:

8.  Exponents of Jacobians and Relative Class Groups, with Borys Kadets   

arXiv | 2024 | pdf 

9.  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

Louis Gaudet, Josh Stucky, and I are co-organizing a special session on "Counting and Asymptotics in Number Theory" at the Spring Eastern AMS Sectional Meeting in April 2025. 

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). As a postdoc, 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.