Akshay Venkatesh

fl. 1981, New Delhi, India

Arithmetic and number theoryAnalysisAlgebraFields Medal 2018

Australian-American number theorist at the Institute for Advanced Study, known for uniting analytic number theory, homogeneous dynamics and representation theory; Fields Medalist 2018.

Akshay Venkatesh was born in New Delhi and raised in Perth, Australia, where he was a child prodigy: he entered the University of Western Australia at 13 and finished an honours degree in mathematics at 16, after winning medals at the International Mathematical Olympiad and the International Physics Olympiad. He earned his PhD at Princeton University in 2002 under Peter Sarnak.

After a Clay Research Fellowship and positions at MIT and the Courant Institute, he joined Stanford University, becoming professor in 2008. In 2018 he moved to the Institute for Advanced Study in Princeton, where he is a permanent faculty member.

His research is unusually hard to confine to one field: he works on L-functions and their subconvexity bounds, automorphic forms, homogeneous dynamics on arithmetic quotients, arithmetic statistics of number fields and class groups, and more recently on the topology and stable cohomology of arithmetic groups and on the arithmetic of periods. A hallmark of his work is importing a method from one area — dynamics, topology, or representation theory — to crack a problem in another. He received the Fields Medal in 2018.

Workplaces: Institute for Advanced Study, Princeton, Stanford University

Australia, United States

Award-winning work

Fields Medal 2018Venkatesh was awarded the medal for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which resolved long-standing problems in areas such as the equidistribution of arithmetic objects. With Philippe Michel he developed a general method for subconvexity bounds on L-functions — estimates that improve on the convexity bound coming from the functional equation — and applied it to equidistribution of arithmetic points. He brought ergodic-theoretic techniques (in the spirit of Ratner's theorems on unipotent flows) to bear on questions about class groups and automorphic forms, and with Einsiedler, Lindenstrauss and Michel made progress on arithmetic equidistribution problems associated with Duke's theorem.

Contributions, linked to the library

Great problemLindelöf hypothesisHis subconvexity bounds for L-functions, developed with Michel, constitute partial progress toward the Lindelöf hypothesis on the growth of L-functions in the critical strip.Great problemLanglands programContributed automorphic and arithmetic methods across the Langlands program, including period integrals and the cohomology of arithmetic groups.Library topicThe Riemann zeta function and the Riemann hypothesisHis estimates on families of L-functions refine our understanding of zeta-type functions and their zeros.