Simon Brendle

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Simon Brendle

Simon Brendle (* June 1981 ) is a German mathematician who deals with partial differential equations of differential geometry .

Career

Brendle won the federal mathematics competition in 1995, 1996 and 1997 and was accepted as a scholarship holder in the German National Academic Foundation . In 2001 he received his doctorate summa cum laude at the University of Tübingen under Gerhard Huisken ( curvature flows on manifolds with a border ). In 2002/2003 he was at the Institute for Advanced Study and then until 2005 Assistant Professor at Princeton University . From 2005 he was Assistant Professor and from 2008 Professor at Stanford University until he moved to Columbia University in 2015 .

Among other things, he was visiting scholar at the ETH Zurich (2008), the University of Cambridge , the University of Paris and the Massachusetts Institute of Technology .

In 2006, Simon Brendle constructed counterexamples to Richard Schoen's compactness conjecture for the Yamabe problem . He also dealt with the Yamabe River and its convergence behavior. In 2007 he proved with Richard Schoen, the differentiable version of the spheres set ( differentiable sphere theorem ). With FC Marques and André Neves, he solved the conjecture of Min-Oo (in three or more dimensions) - it says that an n-dimensional hemisphere with a Riemannian metric of scalar curvature that at least corresponds to the standard metric in a vicinity of the edge Standard metric is isometric . The theorem can be viewed as an analogue in the case of the sphere for the theorem of the positivity of mass in general relativity . In 2012 he proved the Lawson Conjecture and answered a question about the uniqueness of self-similar solutions of the Ricci River . Then he dealt with the Ricci River in higher dimensions. He found a flow-invariant curvature condition and used it to show a higher dimensional version of Perelman's theorem on canonical environments .

In 2012 he received the EMS Prize and gave the Euler Lecture in Sanssouci in 2012. In 2011 he was Takagi Lecturer of the Japanese Mathematical Society and in 2006 he was invited speaker at the International Congress of Mathematicians (ICM) in Madrid ( Elliptic and Parabolic Problems in conformal geometry ) and in 2010 with R. Schoen at the ICM in Hyderabad ( Riemannian manifolds of positive curvature ). In 2006 he was a Sloan Fellow. For 2014 he was awarded the Bôcher Memorial Prize .

Fonts (selection)

  • The set of spheres in Riemann's geometry , Annual Report DMV, Volume 113, 2011, pp. 123-138
  • Global existence and convergence for a higher order flow in conformal geometry , Annals of Mathematics (2), Volume 158-1, 2003, pp. 323-343
  • Elliptic and parabolic problems in conformal geometry , Proceedings of the International Congress of Mathematicians (ICM 2006), Madrid, Spain, August 22-30, 2006. Vol. II, pp. 691-704, 2006
  • Blow-up phenomena for the Yamabe equation , Journal of the AMS 21, pp. 951-979, 2008
  • Convergence of the Yamabe flow in dimension 6 and higher , Inventiones Mathematicae 170, pp. 541-576, 2007
  • with R. Schoen Manifolds with 1/4 pinched curvature are space forms , Journal of the AMS, Vol. 22, 2009, p. 287 (Differentiable Sphere Theorem)
  • Ricci Flow and the Sphere Theorem , American Mathematical Society, Graduate Studies in Mathematics, Volume 111, 2010
  • with R. Schoen Curvature, sphere theorem and the Ricci flow , Bulletin AMS, Volume 48, 2011, pp. 1-32, online
  • with R. Schoen Riemannian manifolds of positive curvature , Proceedings of the International Congress of Mathematicians (ICM 2010), Hyderabad, India, August 19--27, 2010. Vol. I, pp. 449-475, 2011
  • with FC Marques, A. Neves Deformations of the hemisphere that increase scalar curvature , Inventiones Mathematicae, Volume 185, 2011, pp. 175–197, preprint (Min-Oo presumption)
  • Rotational symmetry of self-similar solutions to the Ricci flow , Invent. Math. 194 (2013), no.3, 731-764. Preprint
  • Embedded minimal tori in and the Lawson conjecture , Acta Math. 211 (2013), no. 2, 177-190. Preprint (Lawson conjecture)
  • Embedded self-similar shrinkers of genus 0 , Annals of Mathematics 183, 715–728 (2016)
  • with G. Huisken Mean curvature flow with surgery of mean convex surfaces in R 3 , Invent. Math. 203 (2016), 615-654
  • with G. Huisken A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds , Invent. Math. 210 (2017), 559-613
  • Ricci flow with surgery in higher dimensions , Annals of Mathematics, Volume 187, 2018, pp. 263-299
  • Ricci flow with surgery on manifolds with positive isotropic curvature , Annals of Mathematics 190, 465-559 (2019)

literature

Web links

Individual evidence

  1. ↑ Marathon for Mathemanen , Die Zeit, 16/1996, April 12 1996th
  2. ^ Mathematics Genealogy Project
  3. ↑ Laudation for EMS Prize
  4. ↑ Euler Lecture 2012
personal data
SURNAME Brendle, Simon
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH June 1981