About Ashvin Swaminathan

Born in New Providence, New Jersey, Ashvin A. Swaminathan is the son of Indian immigrants who embody the American Dream. From his parents, both of whom earned graduate degrees in the United States after spending the first twenty years of their lives in economic hardship, Ashvin has learned to be grateful for the freedoms and opportunities that the US has afforded him.

He was the valedictorian of his high school class and received early election to Phi Beta Kappa as an undergraduate. While Ashvin has demonstrated a strong commitment to excellence in a broad range of academic subjects, mathematics is the love of his life, and he aspires to become a math professor. As an undergraduate at Harvard University, he has not only authored ten research papers on a diverse collection of mathematical topics, receiving the Frank and Brennie Morgan Prize for his work, but has also served as a teaching fellow for six advanced math courses and has won prizes for excellence in teaching.

Having graduating from Harvard with degrees in both mathematics and physics, Ashvin is currently pursuing a PhD in mathematics at Princeton University under the supervision of Manjul Bhargava. The focus of his current research is arithmetic statistics, with an emphasis on applications to studying the Cohen-Lenstra heuristics and Diophantine equations. In his future career as a professor, he would like to work together with his students to develop a successful research program within arithmetic statistics. Through his teaching, Ashvin hopes to realize his conviction that mathematics has the power to unify people of diverse backgrounds and interests under the common banner of seeking truth, depth, and wisdom in all their pursuits.

Education

PhD in Mathematics, Princeton University
MA, Harvard University
BA in Mathematics, Harvard University

Professional Fields

Work History

Researcher (mentors: Ken Ono and Jesse Thorner), Emory University, NSF Summer Math REU
Course Assistant, Department of Mathematics, Harvard University
Researcher (mentor: Joseph Gallian), University of Minnesota, NSF Summer Math REU

Milestones and Recognition

Frank and Brennie Morgan Prize, 2018
Centennial Fellowship, Princeton University
Finalist, Fannie and John Hertz Fellowship, 2017
Phi Beta Kappa (Junior 24), 2016
Barry M. Goldwater Scholarship, 2016
Robert Fletcher Rogers Prize, Department of Mathematics, Harvard University, 2016
Harvard University Certificate for Distinction in Teaching, [Math 123, Math 114, Math 131]
John Harvard Scholar, Harvard University, 2014-2016
Detur Book Prize for Academic Excellence, Harvard University, 2014
Valedictorian, The Harker School, 2013
National Winner, Siemens AP Science Award, 2013
National Merit Scholar
Barry Goldwater Scholarship
National Science Foundation Graduate Research Fellow
Appendix to: An arithmetic count of the lines meeting four lines in P3 (with Borys Kadets, Padmavathi Srinivasan, Libby Taylor, and Dennis Tseng), submitted for publication, 2 pages, 2019.
Hyperelliptic curves with maximal Galois action on the torsion points of their Jacobians (with Aaron Landesman, James Tao, and Yujie Xu), to appear in Indiana University Mathematics Journal, 23 pages, 2018.
Linnik’s theorem for Sato-Tate laws on elliptic curves with complex multiplication (with Evan Chen and Peter Park), Research in Number Theory, 1(1) (2015), 1-11. (arXiv)
Average torsion in the ideal groups of rings associated to binary forms (with Arul Shankar, Artane Siad, and Ila Varma), in preparation, 2020.
Average 2-torsion in class groups of rings associated to binary n-ic forms, in preparation, 2020.
Surjectivity of Galois representations in rational families of abelian varieties (with Aaron Landesman, James Tao, and Yujie Xu), Algebra and Number Theory, 13(5) (2019), 995-1038. (arXiv)
Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem (with Evan Chen and Peter Park), International Journal of Number Theory, 14(1) (2018), 255-288. (arXiv)
Permutations that destroy arithmetic progressions in elementary p-groups (with Noam D. Elkies), Electronic Journal of Combinatorics, 24(1) (2017), 1-10. (arXiv)
Lifting subgroups of symplectic groups over Z/lZ (with Aaron Landesman, James Tao, and Yujie Xu), Research in Number Theory, 3(14) (2017), 1-12. (arXiv)
On logarithmically Benford sequences (with Evan Chen and Peter Park), Proceedings of the American Mathematical Society, 144(11) (2016), 4599-4608. (arXiv)
On arboreal Galois representations of rational functions, Journal of Algebra, 448 (2016), 104-126. (arXiv)
Most integral odd-degree binary forms fail to properly represent a square, submitted for publication, 42 pages, 2020.
On the A1-Degree of a Weyl Cover (with Joseph Knight and Dennis Tseng), submitted for publication, 14 pages, 2019.
Inflectionary invariants for isolated complete intersection curve singularities (with Anand Patel), to appear in Memoirs of the American Mathematical Society, 90 pages, 2020.
Analysis on surreal numbers (with Simon Rubinstein-Salzedo), Journal of Logic and Analysis, 6(5) (2014), 1-39. (arXiv)