# Professor Akshay Venkatesh Awarded 2018 Fields Medal

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The International Mathematical Union (IMU) has awarded a 2018 Fields Medal to Akshay Venkatesh, a world-leading mathematician recently appointed to the permanent Faculty of the Institute for Advanced Study (IAS) School of Mathematics. This highest honor was presented to Venkatesh today at the International Congress of Mathematicians (ICM) in Rio de Janeiro “for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.”

“The Fields Medal is an incredible honor for a young mathematician, and the Institute is exceptionally pleased that Akshay Venkatesh has received this most deserved recognition,” said Robbert Dijkgraaf, Director and Leon Levy Professor. “Akshay is an extraordinarily talented mathematician whose profound and diverse contributions underscore his leadership in the field. As a Professor at the Institute, he will help shape the direction of mathematics as a whole.”

Of the 60 individuals who have received the Fields Medal as of 2018, 42 have been affiliated with the Institute. The Fields Medal is awarded every four years to scholars less than 40 years old on the occasion of the ICM to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.

The IMU recognizes Venkatesh for his “contributions to an exceptionally broad range of subjects in mathematics, including number theory, homogeneous dynamics, representation theory, and arithmetic geometry. He solved many longstanding problems by combining methods from seemingly unrelated areas, presented novel viewpoints on classical problems, and produced strikingly far-reaching conjectures.”

On receiving the medal, Venkatesh commented, “It is a great honor to receive this prize. I have had wonderful collaborators, and my work builds on that of many others. This award recognizes their work too!”

The breadth and richness of Venkatesh’s work, as well as the ease with which he works with mathematicians in different fields, has resulted in a large worldwide following, especially among young mathematicians.

He has made fundamental contributions to various fields of mathematics, working in particular at the intersection of analytic number theory, algebraic number theory, and representation theory, continuing the tradition of the groundbreaking work carried out by Armand Borel, Harish-Chandra, Atle Selberg, Carl Siegel, André Weil, and Hermann Weyl in the School of Mathematics. Venkatesh's work further builds on the conjectures of Robert Langlands, Professor Emeritus in the School, relating automorphic forms on general arithmetic locally symmetric spaces and Galois representations.

His many breakthroughs include ones in automorphic forms and representation theory, ergodic theory, and algebraic topology. The signature of his work is great originality and intuition coupled with the development of powerful and general techniques in novel and unexpected settings. As a result, his developments on long-standing problems in number theory have a broad impact in related areas.

As Distinguished Visiting Professor in the Institute’s School of Mathematics in 2017–18, Venkatesh led a special program on analytical and topological aspects of locally symmetric spaces. As part of the special program, he delivered a series of lectures on recent conjectures that have related the cohomology of locally symmetric spaces to the motivic cohomology of algebraic varieties, which he has verified in various special cases. They provide, among other things, new algebraic structures (in the context of non-Shimura varieties) related to the method of Professor Richard Taylor and former Distinguished Visiting Professor Andrew Wiles for analyzing deformations of Galois representations.

Venkatesh earned a B.Sc. in Mathematics and Physics at the University of Western Australia (1997) and a Ph.D. in Mathematics at Princeton University (2002), where his thesis advisory was Peter Sarnak, a Professer at the Institute. He was C.L.E. Moore Instructor (2002–04) at the Massachusetts Institute of Technology, a Member (2005–06) in the Institute’s School of Mathematics, Associate Professor (2005–08) at New York University’s Courant Institute of Mathematical Sciences, and Professor of Mathematics at Stanford University (2008–18). His research has been recognized with many awards, including the Ostrowski Prize (2017); the Infosys Prize (2016); the SASTRA Ramanujan Prize (2008); and the Salem Prize (2007). He serves on the Editorial Boards Committee of the American Mathematical Society and is an editor of the Journal de l'institut mathematique de Jussieu and former editor (2011–16) of Math Annalen.

**About the International Mathematical Union**

The International Mathematical Union is an international non-governmental and non-profit scientific organization, with the purpose of promoting international cooperation in mathematics as well as supporting other international mathematical activities considered likely to contribute to the development of mathematical science in any of its aspects, pure, applied, or educational.

The International Mathematical Union grants four prizes for mathematical achievement which are awarded every four years at the Opening Ceremony of the International Congress of Mathematicians. In addition to the Fields Medal this includes the Rolf Nevanlinna Prize, Carl Friedrich Gauss Prize, and Chern Medal Award.

**About the Institute**

The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. The Institute exists to encourage and support curiosity-driven research in the sciences and humanities—the original, often speculative thinking that produces advances in knowledge that change the way we understand the world. Work at the Institute takes place in four Schools: Historical Studies, Mathematics, Natural Sciences, and Social Science. It provides for the mentoring of scholars by a permanent Faculty, and it ensures the freedom to undertake research that will make significant contributions in any of the broad range of fields in the sciences and humanities studied at the Institute.

The Institute, founded in 1930, is a private, independent academic institution located in Princeton, New Jersey. Its more than 8,000 former Members have held positions of intellectual and scientific leadership throughout the academic world. Thirty-three Nobel Laureates and 42 out of 60 Fields Medalists, as well as many winners of the Wolf and MacArthur prizes, have been affiliated with the Institute.