Daniel Keliher
Tufts University Dept. of Mathematics
BromfieldPearson 207
daniel (dot) keliher (at) tufts.edu



Info
I am a thirdyear 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 S_{4} and D_{4} extensions of a number field. Over Q, it's known that about 83% of quartic extensions have associated Galois group S_{4}, while only about 17% have associated Galois group D_{4}. Contrasting with the case over Q, we find that over quadratic fields, D_{4} extensions can far outweigh S_{4} extensions. I am also very interested in analagous questions over function fields.
 Comparing the Density of D_{4 }and S_{4 }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 DanaFarber Cancer Insitute. My contributions primarily dealt with applications of nonnegative 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 microsatellitestable solid tumors. Nature Genetics (2018)
 D. Liu, P. Abbosh, D. Keliher, et al. Mutational patterns in chemotherapy resistant muscleinvasive bladder cancer. Nature Communications (2017)
Teaching
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 MATH0061: Discrete Math, Spring 2019 and Fall 2019
 Instructor of Record for MATH0030: Introduction to Calculus, Summer II 2019
 Recitation Instructor for MATH0032: Calculus I, Fall 2019
 Instructor for a summer session math standardized test prep course, Summer 2018
 TA for MATH0146: Abstract Algebra 2, Spring 2018
 TA for MATH0145: 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.
Travel
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)
 † MaineQuebec Number Theory Conference (UMaine, October 2019)
 CMIHIMR 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)
 MaineQuebec 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)
 MaineQuebec Number Theory Conference (UMaine, October 2017)
(† I spoke at these conferences)
Links
"General Bourbaki"?