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 [arXiv, slides, journal; Proceedings of the American Mathematical Society, 2021]

2. Enumerating  D4  Quartics and a Galois Group Bias Over Function Fields [arXiv, slides, journal; Journal de Théorie des Nombres de Bordeaux, 2022]

3. Mertens' Theorem for Chebotarev Sets, with Santiago Arango-Piñeros and Chris Keyes [arXiv, journal; International Journal of Number Theory, 2022]

4.  Rank Growth of Elliptic Curves in S4  and A4  Extensions of the Rationals [arXiv, slides; submitted 2022]

5. Exceptional Biases over Function Fields, with Alexandre Bailleul, Lucile Devin and Wanlin Li [arXiv, slides; submitted 2023]

6. Optimal Transport for Some Symmetric Multidimensional Partitions, with Daniel Adu [preprint; submitted 2023]

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)

Other Stuff

For many years I organized the Tufts University Directed Reading Program (DRP). In Fall 2022, I participated in the Spelman-Morehouse DRP. 

From Spring 2019 to Fall 2021, I organized  the Tufts Math Graduate Student Seminar, which is now run by J.C. Wang.