Fernando Codá Marques

Fernando Codá Marques (born October 8, 1979 ) is a Brazilian mathematician who deals with differential geometry with applications in geometric theory of partial differential equations and general relativity. He is at the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro .

Marques studied mathematics at the Universidade Federal de Alagoas Maceio in Alagoas and at the IMPA with a diploma in 1999 with Bruno César Scardua and received his doctorate in 2003 from Cornell University with José F. Escobar ( Existence and compactness theorems on conformal deformations of metrics ). He was then Assistant Professor at IMPA with a full professorship since 2010. As a post-doctoral student , he was at Stanford University in 2005/6 . In 2014 he moved to Princeton University as a professor .

In 2012 he announced the proof of the Willmore conjecture with André Neves . Thomas Willmore hypothesized that the Willmore energy for tori immersed in three-dimensional Euclidean space is greater than or equal . Neves and Marques proved this with the Min-Max theory of minimal surfaces . Partly in collaboration with Simon Brendle, he deals with problems surrounding the (now solved) Yamabe problem (named after Hidehiko Yamabe ) and applied Grigori Perelman's and Richard S. Hamilton's theory of the Ricci River , for example in the proof that the The modular space of metrics with positive scalar curvature is path- related on compact orientable 3-manifolds . ${\displaystyle 2{\pi }^{2}}$

In 2008 he was at the Institute for Advanced Study and he was visiting scholar at Stanford and Princeton University , the Institut Fourier in Grenoble, the Institut Henri Poincaré , the École polytechnique and the University of Paris-East .

In 2012 he received the Union Matematica de America Latina y el Caribe (UMALCA) Prize, the Third World Academy of Sciences (TWAS) Mathematics Prize and the ICTP Ramanujan Prize . In 2009 he became a member of the Brazilian Academy of Sciences. For 2016 he was awarded the Oswald Veblen Prize . He is a fellow of the American Mathematical Society .

He was invited speaker at the International Congress of Mathematicians 2010 in Hyderabad ( Scalar curvature, conformal geometry and the Ricci flow with surgery ) and was selected as plenary speaker for the ICM 2014 in Seoul ( Minimal surfaces - variational theory and applications ).

Fonts

• with Simon Brendle, André Neves Deformations of the hemisphere that increase scalar curvature , Inventiones Mathematicae 185, 2011, 175–197 (refutation of Min-Oo's conjecture in 3 and more dimensions), Arxiv
• Deforming three-manifolds with positive scalar curvature , Annals of Mathematics 176 (2012), 815-863, Arxiv
• with Neves: Min-max theory and the Willmore conjecture. Annals of Mathematics 179 (2014), 683-782.
• with Lyokumovich, Neves: Weyl law for the volume spectrum. Annals of Mathematics 187 (2018), 933-961.
• with Brendle: Recent progress on the Yamabe Problem, in Surveys in Geometric Analysis and Relativity , 2011 (Richard Schoen on his 60th birthday), Arxiv
• with Neves: The Willmore Conjecture, Annual Report DMV, Volume 116, Issue 4, 2014, pp. 201–222

Web links

• Website at IMPA

Individual evidence

1. ↑ Fernando Codá Marques in the Mathematics Genealogy Project (English)
2. ^ Min-Max Theory and the Willmore Conjecture . Appears in Annals of Mathematics.
3. ↑ Neves (Imperial College) received the Whitehead Prize in 2013