Akshay Venkatesh Quanta — Sasha Maslov / Quanta Magazine

Echoes of Electromagnetism Found in Number Theory

This July, Akshay Venkatesh, Robert & Luisa Fernholz Professor in the School of Mathematics, posted a 451-page manuscript, on which he collaborated with two past Members in the School, David Ben-Zvi (2008, 2018) and Yiannis Sakellaridis (2011, 2017–18). The manuscript "makes progress on a long-held dream within a sweeping research initiative in mathematics called the Langlands program."

"The Langlands program was initiated by Robert Langlands, now a Professor Emeritus at the Institute for Advanced Study. It started in 1967 as a 17-page handwritten letter from Langlands, then a young professor at Princeton University, to [past IAS Faculty] André Weil (1958–98), who was one of the best-known mathematicians in the world."

"Mathematicians working on questions in the program seek to build bridges between disparate areas to show how advanced forms of calculus (where periods originate) can be used to answer fundamental open questions in number theory (the home of L-functions), or how geometry can be brought to bear on basic questions in arithmetic."

"The new paper is one of the first to link the geometric and arithmetic sides of the program, which for decades have advanced largely in isolation from each other. By creating this link, and effectively enlarging the scope of the Langlands program as it was originally conceived, the new paper provides a single conceptual framework for a slew of mathematical connections."