### Daniel Keliher (he/him)

### Limited Term Assistant Professor

### University of Georgia

### Dept. of Mathematics

## About

I am presently a limited term assistant professor at the 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 supervised by Robert Lemke Oliver.

In Fall 2024, I will be joining the Concourse program at MIT as a lecturer in mathematics.

I can be reached at mylastname(at)uga(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 UGA, Fall 2023

Instructor of Record for Math 2225: Calculus 1, Spring 2024 (2 sections)

Past Teaching at UGA

Instructor of Record for Math 4450/6450: Cryptology and Computational Number Theory, Fall 2023

Instructor of Record for Math 2260: Calculus II, Spring 2023

Instructor of Record for Math 2250: Calculus I, Fall 2022 (2 sections)

Past Teaching at Salve Regina:

Instructor of Record for MTH-171-02: Mathematics in the Social Sciences, Spring 2021

Past Teaching at Tufts:

Head TA + TA for Math 32 recitation, AY2021

Instructor of Record for MATH-0019: Mathematics of Social Choice, Summer 2021

Instructor of Record for MATH-0021: Introductory Statistics, Spring 2020 and Summer B 2020 (syllabus)

Instructor of Record for MATH-0030: Introduction to Calculus, Summer 2019

Recitation Instructor for MATH-0032: Calculus I, Fall 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.