## About

I am presently the mathematics lecturer for the Concourse program at MIT. Previously, I was a postdoc at University of Georgia working with Jiuya Wang and with the Arithmetic Geometry and Number Theory Group. Broadly speaking, my interests include number theory and arithmetic statistics. I received my PhD in mathematics from Tufts University, where I was advised by Robert Lemke Oliver, in 2022.

I can be reached at mylastname(at)mit(dot)edu. Here is my CV.

## 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:

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

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

Enumerating D4 Quartics and a Galois Group Bias Over Function Fields

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

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

International Journal of Number Theory | 2022 | pdf | journal

Optimal Transport for Some Symmetric Multidimensional Partitions, with Daniel Adu

Discrete Applied Mathematics | 2023 | pdf | journal

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

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:

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

Submitted | 2022 | pdf | slides

Dominant Galois Groups for Large Degree Extensions, with Jiuya Wang

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:

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

Nature Communications | 2017 | journal

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

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

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

Nature Cancer | 2021 | journal

## Teaching

Teaching at MIT

CC.18.02: Concourse Multivariable Calculus, Fall 2024

CC.18.03: Concourse Differential Equations, Spring 2025

Past Teaching at UGA

Math 2225: Calculus 1, Spring 2024, Fall 2022

Math 4450/6450: Cryptology and Computational Number Theory, Fall 2023

Math 2260: Calculus II, Spring 2024

Past Teaching at Salve Regina:

MTH-171-02: Mathematics in the Social Sciences, Spring 2021

Past Teaching at Tufts:

Head TA + Graduate Development Seminar, AY2021

MATH-0019: Mathematics of Social Choice, Summer 2021

MATH-0021: Introductory Statistics, Spring 2020 and Summer B 2020 (syllabus)

MATH-0030: Introduction to Calculus, Summer 2019

## 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.