Daniel Keliher (he/him)

Ph.D Candidate

Tufts University

Dept. of Mathematics

Joyce Cummings Center

Information

I am a fifth-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 myfirstname.mylastname@tufts.edu. Here is my CV.

Starting in Fall 2022, I will be a postdoc at the University of Georgia.

Research

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

  1. Comparing the Density of D4 and S4 Extensions of Number Fields, with Matt Friedrichsen [Proc. Amer. Math. Soc. 149 (2021), 2357-2369; arXiv]

  2. Enumerating D4 Quartics and a Galois Group Bias Over Function Fields [arXiv, accepted by Journal de Théorie des Nombres de Bordeaux]

  3. Mertens' Theorem for Chebotarev Sets, with Santiago Arango-Piñeros and Chris Keyes [arXiv, accepted by International Journal of Number Theory]

  4. Exceptional Biases over Function Fields, with Alexandre Bailleul, Lucile Devin and Wanlin Li [In preparation]


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:

  1. D. Liu, P. Abbosh, D. Keliher, et al. Mutational patterns in chemotherapy resistant muscle-invasive bladder cancer. Nature Communications (2017)

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

  3. 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)

  4. B. Reardon, N. D. Moore, N. Moore, et al. Clinical interpretation of integrative molecular profiles to guide precision cancer medicine (bioRXiv preprint, 2020)

Teaching

Current Teaching, Spring 2022

  • I am not teaching this semester. I am one of two head TAs running the Graduate Development Seminar. First-year participants should check Canvas for details.

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, Spring 2022

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

  • TA for MATH-0063: Transition to Proofs, Spring 2021

  • 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 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.