# Simon Brendle

Simon Brendle
Born June 1981 (age 32)
Nationality German
Fields Mathematics
Institutions Stanford University
Alma mater University of Tübingen
Doctoral advisor Gerhard Huisken
Known for Yamabe Flow, Differentiable Sphere Theorem, Min-Oo Conjecture, Lawson Conjecture
Notable awards EMS Prize (2012), Bôcher Prize (2014)

Simon Brendle (born June 1981) is a German mathematician. He received his Ph.D. from Tübingen University under the supervision of Gerhard Huisken (2001) and is currently a professor at Stanford University. He has held visiting positions at MIT, ETH Zürich, Princeton University, and Cambridge University.

In 2006 he constructed counterexamples to the Compactness Conjecture for the Yamabe problem. He also gave a complete description of the asymptotic behavior of the Yamabe flow. In 2007 he proved the Differentiable Sphere Theorem (joint with Richard Schoen). In a joint work with Fernando Marques and Andre Neves he settled Min-Oo's conjecture. In 2012 he proved the Hsiang–Lawson's conjecture and resolved a problem concerning the uniqueness of self-similar solutions to the Ricci flow which arose in the context of Grigori Perelman's work.

For his contributions to differential geometry he was awarded an EMS Prize in 2012.[1] He delivered the 2012 Euler Lecture and the 2011 Takagi Lectures, and he was an invited speaker at the ICM 2006 in Madrid. He received an Alfred P. Sloan Fellowship in 2006. In December 2013, he was named as the recipient of the Bôcher Prize of the American Mathematical Society.

## 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, 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, pp. 731--764, 2013
• Embedded minimal tori in $S^3$ and the Lawson conjecture, Preprint (Lawson Conjecture)