Victor Ginzburg

Victor Ginzburg
2012 in Oberwolfach
Born 1957 (age 60–61)
Moscow, Russia
Nationality American
Alma mater Moscow State University
Known for Ginzburg dg algebra
Koszul duality
Scientific career
Fields Mathematics
Institutions University of Chicago
Doctoral advisor Alexandre Kirillov
Israel Gelfand

Victor Ginzburg (born 1957) is a Russian American mathematician who works in representation theory and in noncommutative geometry. He is known for his contributions to geometric representation theory, especially, for his works on representations of quantum groups and Hecke algebras, and on the geometric Langlands program (Satake equivalence of categories).

The book "Representation theory and complex geometry", by Neil Chriss and Ginzburg, is nowadays a classical text on geometric representation theory. In an influential paper by Alexander Beilinson, Ginzburg, and Wolfgang Soergel, the authors introduced the concept of Koszul duality (cf. Koszul algebra) and the technique of "mixed categories" to representation theory. Furthermore, Ginzburg and Mikhail Kapranov developed Koszul duality theory for operads.

In noncommutative geometry, Ginzburg defined, following earlier ideas of Maxim Kontsevich, the notion of Calabi–Yau algebra. An important role in the theory of motivic Donaldson–Thomas invariants is played by the so-called "Ginzburg dg algebra", a Calabi-Yau (dg)-algebra of dimension 3 associated with any cyclic potential on the path algebra of a quiver.

Ginzburg received his Ph.D. at Moscow State University in 1985, under the direction of Alexandre Kirillov and Israel Gelfand. He is currently a Professor of Mathematics at the University of Chicago.[1][2]

Selected publications

  • Beilinson, Alexander; Ginzburg, Victor; Soergel, Wolfgang (1996), "Koszul duality patterns in representation theory" (PDF), Journal of the American Mathematical Society, 9 (2): 473–527, doi:10.1090/S0894-0347-96-00192-0, MR 1322847
  • Chriss, Neil; Ginzburg, Victor (1997), Representation theory and complex geometry, Boston, MA: Birkhäuser, MR 1433132
  • Etingof, Pavel; Ginzburg, Victor (2002), "Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism", Inventiones Mathematicae, 147 (2): 243–348, arXiv:math/0011114, Bibcode:2002InMat.147..243E, doi:10.1007/s002220100171, MR 1881922
  • Ginzburg, Victor (2005). "Lectures on Noncommutative Geometry". arXiv:math/0506603.
  • Ginzburg, Victor (2006). "Calabi-Yau Algebras". arXiv:math/0612139.
  • Ginzburg, Victor; Kapranov, Mikhail (1994), "Koszul duality for operads", Duke Mathematical Journal, 76 (1): 203–272, doi:10.1215/S0012-7094-94-07608-4, MR 1301191

References

  1. ↑ Koppes, Steve (June 8, 2006), "Victor Ginzburg, Professor in Mathematics and the College", The University of Chicago Chronicle .
  2. ↑ http://www.ams.org/distribution/mmj/vol7-4-2007/ginzburg-birthday.html

Victor Ginzburg at the Mathematics Genealogy Project

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