Simon Brendle (born June 1981) is a German mathematician working in

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

and nonlinear partial differential equations. He received his

Dr. rer. nat. ''Doctor rerum naturalium'' ( for, , Latin, doctor of natural sciences, lit. 'doctor of the things of nature'), abbreviated Dr. rer. nat., is a doctoral academic degree awarded by universities in some European countries (e.g. Germany, Austria and C ...

from

Tübingen University Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in thre ...

under the supervision of Gerhard Huisken (2001). He was a professor at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

(2005–2016), and is currently a professor at Columbia University. He has held visiting positions at MIT, ETH Zürich, Princeton University, and Cambridge University.

Contributions to mathematics

Simon Brendle has solved major open problems regarding the Yamabe equation in conformal geometry. This includes his counterexamples to the compactness conjecture for the Yamabe problem, and the proof of the convergence of the

Yamabe flow In differential geometry, the Yamabe flow is an intrinsic geometric flow—a process which deforms the metric of a Riemannian manifold. First introduced by Richard S. Hamilton, Yamabe flow is for noncompact manifolds, and is the negative ''L'' ...

in all dimensions (conjectured by Richard Hamilton). In 2007, he proved the

differentiable sphere theorem In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound. The precise statement of the theorem is as follows. ...

(in collaboration with Richard Schoen), a fundamental problem in global differential geometry. In 2012, he proved the Hsiang–Lawson's conjecture, a longstanding problem in minimal surface theory. He has also worked on singularity formation in the

mean curvature flow In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surf ...

and Ricci flow, solving a question concerning the uniqueness of self-similar solutions to the Ricci flow which arose in the context of Grigori Perelman's work.

Honors and awards

For his contributions to

he was awarded an EMS Prize in 2012. He delivered the 2012 Euler Lecture and the 2011 Takagi Lectures. He received an

Alfred P. Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in 2006. In December 2013, he was named as the recipient of the

Bôcher Prize Bocher is a surname. Notable people with the surname include: *Christiane Bøcher (1798–1874), Norwegian stage actress who was engaged at the Christiania Offentlige Theater * Édouard Bocher (1811–1900), French politician who was one of the fou ...

of the American Mathematical Society. In 2017, he received a Simons Investigator Award and the Fermat Prize.

Main publications

*''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 *(joint with R. Schoen) ''Manifolds with 1/4 pinched curvature are space forms'', Journal of the AMS, 22, 2009, pp. 287 (Differentiable Sphere Theorem)
''Ricci Flow and the Sphere Theorem''
American Mathematical Society,

Graduate Studies in Mathematics Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). The books in this series are published ihardcoverane-bookformats. List of books *1 ''The General To ...

, vol. 111, 2010 *(joint with R. Schoen) ''Curvature, sphere theorem and the Ricci flow'', Bulletin of the AMS, 48, 2011, pp. 1–32
Online
*(joint 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 *(joint with F. C. Marques, A. Neves) ''Deformations of the hemisphere that increase scalar curvature'', Inventiones Mathematicae 185, 2011, pp. 175–197
Preprint
(Min-Oo Conjecture) *''Rotational symmetry of self-similar solutions to the Ricci flow'' Inventiones Mathematicae 194, 2013, pp. 731–764 *''Embedded minimal tori in

S^3

and the Lawson conjecture'', Acta Mathematica 211, 2013, pp. 177–190
Preprint
(Lawson Conjecture) *''Embedded self-similar shrinkers of genus 0'', Annals of Mathematics 183, 715-728 (2016
Preprint

References

External links

* {{DEFAULTSORT:Brendle, Simon 1981 births Living people Differential geometers 21st-century German mathematicians University of Tübingen alumni Stanford University Department of Mathematics faculty Sloan Research Fellows Columbia University faculty Simons Investigator