Michael Wolf (mathematician)

from Wikipedia, the free encyclopedia

Michael Wolf (born January 29, 1960 in Philadelphia , Pennsylvania ) is an American mathematician and professor at Rice University .

Michael Wolf studied mathematics and philosophy at Yale University with a bachelor's degree in 1981 and received his doctorate in 1986 from Stanford University under Steven Kerckhoff ( The Teichmüller Theory of Harmonic Maps ). As a post-doctoral student , he was Moore Instructor at MIT from 1986 to 1988 . In 1988 he became assistant professor , 1993 associate professor and 1999 professor at Rice University , where he headed the mathematics faculty from 2005 to 2009. In 1993/94 he was a research professor at MSRI and a member there in 1995 and 2015. In 2013 he was visiting professor at Tsinghua University and in 2005 at Tours University . In 1995 he was a member of the Max Planck Institute for Mathematics in Bonn .

Wolf deals with geometric analysis and global differential geometry , Teichmüller theory , harmonic maps and minimal surfaces . With David Allen Hoffman and Matthias Weber he found a new, completely embedded minimal surface in Euclidean three-dimensional space, a "gender 1 helicoid", which looks like a spiral surface (actually a double spiral) with a hole or tunnel , which is infinitely continued along an axis in the center of a leaf. It has topological gender 1 with one end , i.e. the topology of a dotted torus , and the end is asymptotic to a helicoid . Before, only the plain and the helicoids were known as examples of such minimal surfaces. Both have gender 0 (and are the only such areas after William Meeks III and Harold William Rosenberg ). Embedded geometrically means that it does not intersect itself and completely that it is infinitely extended without a border. A computer model of this surface had already been created in the 1990s (David Hoffman, Fusheng Wei, Hermann Karcher ), but there was no mathematical proof that the surface in the case of genus 1 does not intersect itself. At that time, Hoffman and colleagues even found a whole family of such surfaces with any finite topological gender (albeit also without proof).

He is on the editorial board of the Bulletin of the American Mathematical Society (2016). From 1991 to 1995 he was a Sloan Research Fellow . In 2012 he became a Fellow of the American Mathematical Society .

Fonts

  • The Teichmüller Theory of Harmonic Maps, J. Differential Geom., Volume 29, 1989, pp. 449-479.
  • Infinite Energy Harmonic Maps and Degeneration of Hyperbolic Surfaces in Moduli Space, J. Differential Geom., Volume 33, 1991, pp. 487-539
  • with Scott Wolpert : Real Analytic Structures on the Moduli Space of Curves, Amer. J. Math., Vol. 114, 1992, pp. 1079-1102.
  • with Howard Masur : Teichmüller space is not Gromov hyperbolic, Ann.Acad. Sci. Fenn., Vol. 20, 1995, pp. 259-267
  • with Robert Hardt : Harmonic extensions of quasiconformal maps to hyperbolic space, Indiana J. Math., Volume 46, 1997, pp. 155-163
  • Measured Foliations and Harmonic Maps of Surfaces, J. Differential Geom., Volume 49, 1998, pp. 437-467.
  • with Matthias Weber: Teichmüller Theory and Handle Addition for Minimal Surfaces, Annals of Mathematics, Volume 156, 2002, pp. 713–795.
  • with Matthias Weber: Minimal Surfaces of Least Total Curvature and Moduli Spaces of Plane Polygonal Arcs, Geom. and Funct. Anal., Vol. 8, 1998, pp. 1129-1170.
  • with Matthias Weber, David Allen Hoffman : An embedded genus-one helicoid, Annals of Mathematics, Volume 169, 2009, pp. 347–448 (and Proc. Nat. Acad. USA, Volume 102, 2005, pp. 16566–16568)
  • with Benson Farb : Harmonic splitting of surfaces, Topology, Volume 40, 2001, pp. 1395-1414
  • Flat structures, Teichmüller theory and handle addition for minimal surfaces, in: D. Hoffman (Ed.), Proc. Clay Institute 2001 Summer School on the global theory of minimal surfaces, AMS 2005

Web links

Individual evidence

  1. ↑ Michael Wolf in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Ivars Peterson, Surface Story, Science News, Volume 168, September 17, 2005, pdf
  3. ↑ They also proved that the infinite gender helicoid does not intersect itself. The proof by Hoffman, Weber and Wolf builds on this and uses symmetry transformations of the helicoid to reduce the number of handles from infinity to one.
personal data
SURNAME Wolf, Michael
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH January 29, 1960
PLACE OF BIRTH Philadelphia , Pennsylvania