May 31, 2023
The 2023 Shaw Prize in the Mathematical Sciences was awarded to Vladimir Drinfeld, Harry Pratt Judson Distinguished Service Professor of Mathematics at the University of Chicago, and Shing-Tung Yau, Director of Yau Mathematical Sciences Center at Tsinghua University, PRC, for their contributions related to mathematical physics, to arithmetic geometry, to differential geometry and to Kähler geometry.
Drinfeld’s work is a pillar of arithmetic geometry which is at the core of new developments in the field.
Together with Alexander Beilinson, he launched the geometric Langlands program, which has some common features with aspects of quantum field theory, and yet stems from number theory.
At an early age, Drinfeld invented the shtukas (coming from Stück in German, meaning “piece”) in resonance with the Korteweg–de Vries equation in physics. With it, he solved the arithmetic Langlands program over a function field in rank two, for which he was awarded the Fields Medal in 1990. It was then and there that they noticed his solution proved at the same time a conjecture of Deligne on the existence of compatible ℓ-adic systems in rank two. Remarkably, after the Langlands program over a function field was proven in any rank in 2002 by L Lafforgue, following Drinfeld’s method, Drinfeld could extend the existence of compatible ℓ-adic systems in any rank from function fields to higher-dimensional varieties. This complete solution to the Deligne conjecture has multiple consequences, even in complex geometry.
In today’s p-adic Hodge theory, and in the dreamed Langlands program over a number field, it is expected that Drinfeld’s shtukas should be a key concept as suggested by Scholze’s general conjectures exposed in his ICM 2018 plenary address. Moreover, Drinfeld’s view on Bhatt–Scholze prismatic cohomology and its systems of coefficients led to a new understanding of the theory and to applications.
Vladimir Drinfeld was born in 1954 in Kharkov, Ukraine, USSR (now Kharkiv, Ukraine). He received his Bachelor’s degree and PhD from Moscow State University, USSR in 1974 and 1978 respectively. He was appointed Assistant Professor at Bashkir State University, USSR in 1978 and Lecturer at Kharkov State University in 1980 respectively. He then served as Research Fellow at B Verkin Institute for Low Temperature Physics and Engineering from 1981 to 1998. He has been a Professor of Mathematics at the University of Chicago since 1998. He is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, and a fellow of the Academy of Sciences, Ukraine.