Vladimir Drinfeld

Native spelling: Володимир Дрінфельд / Владимир Дринфельд

fl. 1954, Kharkiv, Ukrainian SSR, Soviet Union

AlgebraGeometryArithmetic and number theoryFields Medal 1990Wolf Prize in Mathematics 2018Shaw Prize in Mathematical Sciences 2023

Ukrainian-born mathematician who founded the theory of quantum groups and proved the $GL_2$ Langlands conjecture over function fields; Fields Medal 1990, Wolf Prize 2018, Shaw Prize 2023.

Vladimir Gershonovich Drinfeld was born in Kharkiv in 1954 into a family of mathematicians and won the Soviet mathematical olympiad at fifteen. He studied at Moscow State University under Yuri Manin, earning his PhD in 1977, then returned to the Verkin Institute for Low Temperature Physics in Kharkiv, where he spent nearly two decades despite the constraints of Soviet academic life.

In the early 1980s, while studying the quantum inverse scattering method, Drinfeld defined what are now called quantum groups and proved the Langlands conjecture for $GL_2$ over function fields via 'shtukas'. His contributions were recognized with the Fields Medal at the 1990 ICM in Kyoto — at 36 he was among its youngest recipients. He also made decisive contributions to the classification of exactly solvable models, quantum affine algebras, and later (with Alexander Beilinson) the geometric Langlands program and the theory of chiral algebras.

After the dissolution of the Soviet Union, Drinfeld moved to the University of Chicago in 1999, where he is the Harry Pratt Judson Distinguished Service Professor. His later work includes contributions to differential graded categories, prismatic-like structures for the Langlands program, and the theory of algebraic stacks over function fields.

Workplaces: Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, University of Chicago

Ukraine, United States

Award-winning work

Fields Medal 1990Drinfeld introduced quantum groups — deformations of universal enveloping algebras now called quantum groups or quantized enveloping algebras — motivated by the quantum inverse scattering method and the Yang–Baxter equation. His notion of quasitriangular Hopf algebras and the quantum double construction gave a systematic algebraic origin for solutions of the Yang–Baxter equation and a new symmetry concept unifying Lie theory with braided tensor categories. In parallel, he proved the Langlands conjecture for

GL_2

over function fields using his 'shtukas', modular objects of his own invention that were later central to the modern Langlands program. The medal recognized work that created two entire fields: quantum groups and the geometric/function-field Langlands correspondence.

Wolf Prize in Mathematics 2018Shared with Alexander Beilinson for groundbreaking work on the geometric Langlands program and algebraic geometry.

Shaw Prize in Mathematical Sciences 2023Shared with Shing-Tung Yau for contributions related to mathematical physics, arithmetic geometry, differential geometry and Kähler geometry.

Contributions, linked to the library

Library topicRepresentation theoryCreator of quantum groups and quantum affine algebras, central objects in modern representation theory.Library topicLie groups and Lie algebrasHis quantized enveloping algebras deform Lie-algebra structure and underlie the quantum inverse scattering method.