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.