Robert Friedman

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Robert Friedman (born April 15, 1955 ) is an American mathematician who studies algebraic geometry .

Robert Friedman grew up near Boston and studied mathematics at Harvard University with a bachelor's and master's degree in 1976, where he received his doctorate from Phillip Griffiths in 1981 (Hodge theory, deformations and the global Torelli problem) . After that, he was at the Columbia University , where he presided from 2001 to 2004 the mathematics faculty. In 1986 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

He deals with algebraic surfaces and vector bundles on them and their topology.

After Simon Donaldson with had given an example of a 4-manifold with two differentiable structures proved John Morgan and Robert Friedman (and independent Christian Okonek and Anthony van de Ven ) that there are infinitely many differentiable structures on this space. They were naturally given by familiar algebraic surfaces. Since these are classified by their Kodaira dimension and the differentiability structure also varied with the Kodaira dimension in all cases, van de Ven assumed that this is a differential topological invariant. This was proven in 1994 by Robert Friedman and Z. Qin in 1994.

In 2014 he received the Mark van Doren Award for Teaching at Columbia University.

Fonts

  • with John Morgan : Smooth Four-Manifolds and Complex Surfaces, Results of Mathematics and their Frontier Areas, Springer 1994
  • Algebraic Surfaces and Holomorphic Vector Bundles, Springer 1998
  • with Armand Borel , John Morgan: Almost commuting elements in compact Lie groups, Memoirs AMS, 2002
  • Editor with John W. Morgan: Gauge theory and the topology of four-manifolds, IAS / Park City Mathematics Institute Lecture notes 1994, AMS 1998
  • Editor with David Morrison: The birational geometry of degenerations, Birkhäuser 1983

Some essays:

  • with John Morgan: On diffeomorphism types of certain algebraic surfaces, 2 parts, J. Diff. Geom., Vol. 27, 1988, pp. 297-369, Project Euclid
  • with John Morgan: Algebraic surfaces and 4-Manifolds, some conjectures and speculations, BAMS, Volume 18, 1988, pp. 1-19
  • with John Morgan: Complex versus differential classification of algebraic surfaces, Topology Appl, Volume 32, 1989, pp 135-137
  • with John Morgan: Holomorphic Principal Bundles Over Elliptic Curves, Part 1,2, 3, Part 2: J. Diff. Geom., Volume 56, 2000, pp. 301-379, Part 1, Arxiv 1998 , Part 2, Arxiv 2000 , Part 3, Arxiv 2001
  • Rank two vector bundles over regular elliptic surfaces, Inv. Math., Vol. 96, 1989, pp. 283-332
  • with ZB Quin: On complex surfaces diffeomorphic to rational surfaces, Invent. Math., Vol. 120, 1995, pp. 81-117
  • Vector bundles and SO (3) invariants for elliptic surfaces, J. AMS, Volume 8, 1995, pp. 29-139
  • with John W. Morgan: Algebraic surfaces and Seiberg-Witten invariants, J. Algebraic Geometry, Volume 6, 1997, pp. 445-479
  • with John Morgan, Edward Witten : Vector bundles and F theory, Comm. Math., Phys., Vol. 187, 1997, pp. 679-743, Arxiv
  • with John Morgan, Edward Witten: Vector bundles over elliptic fibrations, J. Algebraic Geometry, Volume 8, 1999, pp. 297-401, Arxiv 1997

Web links

Individual evidence

  1. ^ Robert Friedman in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Van de Ven, On the differentiable structure of certain algebraic surfaces, Seminaire Bourbaki 667, 1986, Astérisque 145/146 1987
personal data
SURNAME Friedman, Robert
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 15, 1955