**Daniel Keliher**

### Ph.D Candidate

### Tufts University

### Dept. of Mathematics

### Bromfield-Pearson 207

## Information

I am a fourth-year graduate student in mathematics at Tufts University working under the supervision of Robert Lemke Oliver. Broadly speaking, my interests include number theory, arithmetic statistics, and arithmetic geometry. I graduated from Brown in 2017 and earned my Master's from Tufts in 2019. I can be reached at firstname.lastname@tufts.edu.

Starting in the spring semester of 2021, I am also an adjunct faculty member at Salve Regina University.

Here is my CV.

## Research

I am mainly interested in number theory and arithmetic statistics. Here are my papers/preprints:

*Comparing the Density of D*_{4 }*and S*_{4 }*Extensions of Number Fields*, with Matt Friedrichsen (arXiv, accepted by Proc. AMS)*Enumerating**D*_{4 }*Quartics and a Galois Group Bias Over Function Fields*(arXiv, submitted)*Mertens' Theorem for Chebotarev Sets,*with Santiago Arango-Piñeros and Chris Keyes (arXiv, submitted)

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:

D.N. Rodrigues, P. Rescigno, D. Liu, et al.

*Immunogenomic analyses associate immunological alterations with mismatch repair defects in prostate cancer*. The Journal of Clinical Oncology (2019)D. Miao, P. Rescigno, D. Liu, et al.

*Genomic correlates of response to immune checkpoint blockade in microsatellite-stable solid tumors*. Nature Genetics (2018)D. Liu, P. Abbosh, D. Keliher, et al.

*Mutational patterns in chemotherapy resistant muscle-invasive bladder cancer*. Nature Communications (2017)

## Teaching

*Current Teaching,** Spring 2021:*

Tufts University: I am the TA for MATH-0063: Transition to Proofs

Salve Regina University: I am the instructor for MTH-171-02: Mathematics in the Social Sciences (Salve students refer to Canvas for more information, syllabus TBA)

*Past **T**eaching at Tufts:*

TA for MATH-0165: Probability, Fall 2020

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

TA for MATH-0061: Discrete Math, Spring 2019 and Fall 2019

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

Recitation Instructor for MATH-0032: Calculus I, Fall 2019

Instructor for a summer session math standardized test prep course, Summer 2018

TA for MATH-0146: Abstract Algebra 2, Spring 2018

TA for MATH-0145: Abstract Algebra 1, Fall 2017

## Other Stuff

I am currently on the committee organizing the Tufts University Directed Reading Program (DRP).

Since the spring of 2019, I have been organizing the Tufts Math Graduate Student Seminar.