Drinfeld

Vladimir Igorevich Drinfeld (born 1950 in Leningrad, Soviet Union) is a Russian mathematician whose work has profoundly influenced algebra, number theory, and mathematical physics. He is best known for introducing quantum groups and for developing Drinfeld modules, both of which have become central tools in their respective fields. His research has shaped modern approaches to representation theory, arithmetic geometry, and aspects of the Langlands program.

In the 1980s, Drinfeld formulated quantum groups as deformations of universal enveloping algebras equipped with a coproduct, counit, and an R-matrix, providing a rigorous algebraic framework for quantum integrable systems. He introduced the Drinfeld double construction and laid groundwork that connected algebraic structures with topology and mathematical physics. In the setting of function fields, he introduced Drinfeld modules (often described as elliptic modules) as function-field analogues of elliptic curves, a development that has driven advances in arithmetic geometry.

Drinfeld has held research positions in Russia and abroad and has received several honors for his contributions, including the Fields Medal in 1990 for his work on quantum groups. His work continues to influence multiple areas of mathematics, including representation theory, algebraic geometry, and mathematical physics.