Ashvin A. Swaminathan
NSF Postdoctoral Fellow & Benjamin Peirce Fellow
Department of Mathematics, Harvard University
Mentor: Melanie Matchett Wood
Research
My research lies in number theory and algebraic geometry, with a focus on arithmetic statistics, invariant theory, the Cohen-Lenstra heuristics, rational points on varieties, Diophantine equations, and enumerative geometry.
I am increasingly focused on building workflows that combine large language models, symbolic computation, and formal verification to attack research problems in number theory.
Background
I received my AB in mathematics from Harvard College, with a senior thesis supervised by Joe Harris and Anand Patel, as well as an AM in Physics. I completed my MA and PhD at Princeton under Manjul Bhargava.
In Fall 2025, I was on leave from Harvard, participating as a visiting researcher in the special semester on arithmetic statistics at the new Lodha Mathematical Sciences Institute in Mumbai, India.
Outside of mathematics, I love animals and volunteer at Broken Tail Animal Rescue. If you are interested in adopting an animal, please check out their website!
News
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paper
On the quartic invariant of odd-degree binary forms — Preprint. Accompanied by a complete Lean 4 formalization (~15,000 lines).
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talk
Second moments for $2$-Selmer structures on elliptic curves, and applications — Conference on Arithmetic Statistics, Lodha Institute of Mathematical Sciences
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upcoming
Poitou-Tate duality, the 2-Selmer hypercube-graph correspondence, and the Poonen-Rains heuristics — Arithmetic Statistics Seminar, Harvard University
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upcoming
Second moments for $2$-Selmer structures on elliptic curves, and applications — Number Theory Seminar, Harvard University
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upcoming
Positive proportions of elliptic curves with small $2$-Selmer rank, Part II — Workshop on Arithmetic Statistics, Centre de Recherches Mathématiques, Université de Montréal
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upcoming
Positive proportions of elliptic curves with small $2$-Selmer rank — Number Theory Seminar, Boston University