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:

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

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

International Journal of Number Theory | 2022 | pdf | journal 

Discrete Applied Mathematics | 2023 | pdf | journal

Journal of the London Mathematical Society | 2024 | pdf | journal | slides

Proceedings of the Integers Conference 2023  | 2024 | pdf | journal 


Preprints:

Submitted | 2022 | pdf | slides 

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: 

Nature Communications | 2017 | journal 

Nature Genetics  | 2018 | journal 

The Journal of Clinical Oncology | 2019 | journal

Nature Cancer | 2021 | journal

Teaching

Teaching at UGA, Fall 2023 

Past Teaching at UGA

Past Teaching at Salve Regina:

Past Teaching at Tufts:


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