Daniel Keliher

Tufts University Dept. of Mathematics

Bromfield-Pearson 207

daniel (dot) keliher (at) tufts.edu

hello there!


I am a third-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.

Here is my CV.

Research Items

Presently, one of my interests is arithmetic statistics. In particular, Matt Friedrichsen and I are studying the disparity between the number of S4 and D4 extensions of a number field. Over Q, it's known that about 83% of quartic extensions have associated Galois group S4, while only about 17% have associated Galois group D4. Contrasting with the case over Q, we find that over quadratic fields, D4 extensions can far outweigh S4 extensions. I am also very interested in analagous questions over function fields.

  1. Comparing the Density of Dand SExtensions of Number Fields, with Matt Friedrichsen (ArXiv, submitted)
  2. Statistics on Quartic Extensions of Function Fields (in preparation)

Not so long ago, I did some pretty applied things. 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.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)
  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. Liu, P. Abbosh, D. Keliher, et al. Mutational patterns in chemotherapy resistant muscle-invasive bladder cancer. Nature Communications (2017)


Current, Spring 2020: I am teaching a section of Math 21: Introduction to Statistics. Information about the course can be found on the Canvas page or on the syllabus.

Past teaching at Tufts:

Undergraduate TA Experience:

Stuff I help(ed) organize


I have attended or will attend the following conferences:

(† I spoke at these conferences)


Edward Kassar    "General Bourbaki"?