Fields Medalist

Vladimir Gershonovich Drinfel’d was born on the 14^th of February in 1954. His home town was Kharkov. In 1969, at the age of 15, Vladimir Drinfel’d represented the Soviet Union at the International Mathematics Olympiad in Bucharest, Romania (the first IMO), and won a gold medal with the full score of 40 points. The same year he entered Moscow State University and graduated from it in 1974. Then at the age of twenty, Drinfel’d announced a proof of the Langland’s conjectures. In the course of proving the conjectures, Drinfel’d introduced a new class of objects which he called Elliptic modules. Since that time these modules have also become known as shtukas and Drinfel’d modules. In 1978 Drinfel’d was awarded the Candidate of Sciences degree. He became a researcher at the Institute of Physics of Low Temperatures of the National Academy of Sciences of Ukraine in Kharkiv. In 1983 Drinfel’d published a short article that expanded the scope of the Langland’s conjectures. His work related algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langland’s correspondence. Later in collaboration with his advisor Yuri Manin, he achieved a new result which was independently proved by Michael Atiyah and Nigel Hitchin. In 1986 at the International Congress of Mathematicians he coined the term "Quantum group"" in reference to Hopf algebra and connected it to the study of the Yang–Baxter equation, which was a necessary condition for the solvability of statistical mechanical models. He also generalized Hopf algebra to quasi-Hopf algebra, and introduced the study of ‘Drinfel’d twists’, which can be used to factorize the R-matrix corresponding to the solution of the Yang–Baxter equation associated with a quasi-triangular Hopf algebra. He introduced the notion of a quantum group (independently discovered by Michio Jimbo at the same time). In 1988 he was awarded Doctor of Sciences degree from the Steklov Mathematical Institute.

Later Drinfel’d moved to mathematical physics. He made important contributions into mathematical physics, including algebraic formalism of the Quantum Inverse Scattering Method. In 1990 he was awarded the Fields Medal. In 1992 Drinfel’d was elected a corresponding member of the National Academy of Sciences of Ukraine.

Currently, Drinfel’d is the Harry Pratt Judson Distinguished Service Professor at the University of Chicago.

Drinfel’d has also collaborated with Alexander Beilinson to rebuild the theory of vertex algebras which has become increasingly important to conformal field theory, string theory and the geometric Langland’s program. His new work dealing with algebra appeared in a book form in 2004.

I. Decide if the given statement is true (T) according to the text, if it is false (F) or if the information is not given (NG)in the text (Work in pairs)

1. Vladimir Drinfel’d was a representative of Ukraine at the first International Mathematics Olympiad.

2. In 1974 Drinfel’d gave birth to Drinfel’d modules.

3. Firstly he was interested in algebraic geometry, but later he worked in the field of mathematical physics.

4. He was the first to discover a quantum group in collaboration with Michio Jimbo.

5. The introduction of Drinfel’d twists made it possible to factorize the R-matrix.

6. He was awarded Fields Medal due to his great contributions into mathematical physics.

7. He is known to be elected an honorable member of the National Academy of Sciences of Ukraine.

8. At present he delivers lectures at some universities in the US.

9. In order to rebuild the theory of vertex algebras Drinfel’d began working with Alexander Beilinson.

10. Finally, in 2004 his new work was published.