Tufts University Dept. of Mathematics
daniel (dot) keliher (at) tufts.edu
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.
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.
- Comparing the Density of D4 and S4 Extensions of Number Fields, with Matt Friedrichsen (ArXiv, submitted)
- 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:
- 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)
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:
- 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
Undergraduate TA Experience:
- TA for MATH0540: Honors Linear Algebra, Spring 2017 (Brown)
- TA for MATH0158: Cryptography, Fall 2015 (Brown)
- TA for MATH0190: Advanced Placement Calculus, Fall 2014 (Brown)
Stuff I help(ed) organize
- 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 (Eminar).
- As an undergrad, I helped run the Brown University Symposium for Undergraduates in the Mathematical Sciences (SUMS) in 2016 and 2017.
I have attended or will attend the following conferences:
- Tufts University Graduate Student Summer Speaker Series, (Virtual, June 2020)
- Modular Forms, Arithmetic, and Women in Mathematics (Emory U., November 2019)
- Midwest Arithmetic Geometry and Number Theory Series (Ohio State, October 2019)
- Maine-Quebec Number Theory Conference (UMaine, October 2019)
- CMI-HIMR Summer School in Computational Number Theory (University of Bristol, June 2019)
- PIMS Workshop in Arithmetic Topology (University of British Columbia, June 2019)
- Grad Student Conference in Algebra, Geometry and Topology (Temple, June 2019)
- Upstate Number Theory Conference (Cornell, April 2019)
- Arizona Winter School (U. Arizona, March 2019)
- Palmetto Number Theory Series XXI (U. South Carolina, December 2018)
- Maine-Quebec Number Theory Conference (U. Laval, October 2018)
- 2018 Chicago Summer Workshop: The roots of topology: miracles of algebraic geometry, braids and Hilbert's (still open) 13th problem (UChicago, June 2018)
- Connecticut Summer School in Number Theory/Arithmetic Geometry and Number Theory Conference (UConn, June 2018)
- 32nd Automorphic Forms Workshop (Tufts, March 2018)
- Maine-Quebec Number Theory Conference (UMaine, October 2017)
( I spoke at these conferences)