## 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

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

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

Preprints:

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

Math2225: Calculus 1, Spring 2024, Fall 2022

Math4450/6450: Cryptology and Computational Number Theory, Fall 2023

Math2260: Calculus 2, 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.