The 17th Atul Vyas Memorial Lecture in Mathematics — Alexander Dunn (Georgia Institute of Technology)

Atul Vyas was an outstanding CMC student who was majoring in Mathematics and Physics. He tragically lost his life in a train crash that occurred on September 12, 2008 in Chatsworth, California. The Mathematical Sciences Department at CMC fondly remembers Atul as someone who was equally excited by the power of mathematical abstraction and the possibilities for its applications.

In memory of Atul, the CMC Mathematical Sciences Department hosts a yearly lecture series, aimed at a general audience, on the Creative Application of Abstract Mathematical Ideas.

Location: Davidson Lecture Hall, CMC

Time: 4:30pm-5:30pm, Thursday, November 19.

Refreshments will be served prior to the talk starting at 4:15pm.

Click here for the poster for this event.

Alexander Dunn (Georgia Institute of Technology)

Alexander Dunn is the Richard A. Duke Assistant Professor in the School of Mathematics at the Georgia Institute of Technology, where he has been on the faculty since 2023. Originally from Australia, he earned his bachelor’s degree, with a University Medal, and a Master of Philosophy at the University of Queensland, and his Ph.D. from the University of Illinois at Urbana–Champaign in 2020 under the supervision of Scott Ahlgren and Alexandru Zaharescu. From 2020 to 2023 he was an Olga Taussky and John Todd Instructor in Mathematics at Caltech.

Dunn works in analytic number theory, with interests including automorphic and metaplectic forms, L-functions, exponential sums, and primes. Dunn received the 2024 SASTRA Ramanujan Prize for his contributions to number theory, and in 2026 he received a Frontiers in Science Award from the International Congress of Basic Science.

Title: From cubic Gauss sums to the quasi-Riemann hypothesis

Abstract: Gauss sums are sums of roots of unity that arise in counting solutions to polynomial equations modulo a prime. Their normalized values can be uniformly distributed and still have a bias on a smaller scale. This distinction helps explain a puzzle about cubic Gauss sums that began with Kummer’s hand calculations in 1846 and was revisited on the Institute for Advanced Study’s early electronic computer in 1953. Patterson’s conjecture of 1978 makes the bias precise. Maksym Radziwiłł and I proved it under the generalized Riemann hypothesis in 2024.

The Riemann hypothesis would give a precise bound on the error in approximating the number of primes up to a given size. The methods developed for the Gauss sum problem have now found an unexpected use in OpenAI’s 2026 proof of an \(11/12\) quasi-Riemann hypothesis. I will explain how our unconditional summation formulae are used in the proof, and discuss the earlier ideas it relies on and the mathematicians who developed them.