nLab Vladimir Drinfel'd

Vladimir Gershonovich Drinfel’d (Russian: Владимир Гершонович Дринфельд, Ukrainian: Володимир Гершонович Дрінфельд) is an Ukrainian-born (Feb 4, 1954) mathematician, recipient of Fields Medal (1990), now a professor at the University of Chicago. He was student of Yuri Manin at Moscow; his main specialty is algebraic geometry, including applications to arithmetic, automorphic forms, representation theory and mathematical physics. His famous discoveries and new concepts Drinfel’d modular varieties, Drinfel’d shtukas (Drinfel’d elliptic modules), ADHM-construction of instantons, Drinfel'd-Sokolov reduction in the theory of integrable systems, algebraic approach to quantum inverse scattering method in integrable systems, and related subject of quantum groups including Yangians and quasi-Hopf algebras, geometric Langlands program, chiral algebras (with A. Beilinson), certain category of infinite-dimensional bundles in algebraic geometry (now sometimes called Drinfel’d bundles), and the general construction of quotient dg-categories in homological algebra. His ideas also influenced the beginnings of the new subject of derived algebraic geometry.

• wikipedia

Selected writings

Introducing the ADHM construction for Yang-Mills instantons:

• Michael Atiyah, Nigel Hitchin, Vladimir Drinfeld, Yuri Manin, Construction of instantons, Physics Letters A 65 3 (1978) 185-187 [doi:10.1016/0375-9601(78)90141-X]

Introducing quantum groups and the Drinfeld double-construction:

• Vladimir Drinfeld, Quantum groups, in: A. Gleason (ed.) Proceedings of the 1986 International Congress of Mathematics 1 (1987) 798-820 [pdf]

  expanded version:

  Journal of Soviet Mathematics 41 (1988) 898–915 [doi:10.1007/BF01247086]

On chiral algebras:

• A. A. Beilinson, V. Drinfeld, Chiral Algebras, AMS 2004 (the final form of a preprint in various forms since around 1995, cf. here).

On braided fusion categories:

• Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik, On braided fusion categories I, Selecta Mathematica. New Series 16 (2010), no. 1, 1–119 (doi:10.1007/s00029-010-0017-z)

On prismatic cohomology

• Vladimir Drinfeld, Prismatization (arXiv:2005.04746)

category: people