Occupation | Mathematician |

Country | Brazil |

Social | |

Date of birth | São Carlos, São Paulo, Brazil |

Awards | Oswald Veblen Prize in Geometry, The World Academy of Sciences (TWAS) Prize |

Education | Cornell University, Instituto Nacional de Matemática Pura e Aplicada |

Fernando Codá dos Santos Cavalcanti Marques (born 8 October 1979) is a Brazilian mathematician working mainly in geometry, topology, partial differential equations and Morse theory. He is a professor at Princeton University. In 2012, together with André Neves, he proved the Willmore conjecture.

## Biography

Fernando Codá Marques was born on 8 October 1979 in São Carlos and grew up in Maceió. His parents were both professors of engineering.

Codá Marques started as a student of civil engineering at the Federal University of Alagoas in 1996, but switched to mathematics after two years.

He obtained a master's degree from the IMPA in 1999. Among his teachers at the IMPA were Manfredo do Carmo and Elon Lages Lima.

Following the advice of Manfredo do Carmo, Codá Marques went to Cornell University to learn geometric analysis from José F. Escobar, so that he could return and bring this area of research to Brazil. While still in Brazil, Codá Marques had been informed that Escobar was facing cancer and that he could maybe die before Codá Marques could complete his Ph.D with him. Despite this information, Codá Marques decided to keep the arrangement and became his student.

In 2001, Codá Marques was awarded Cornell's Battig Prize for graduate students, for "excellence and promise in mathematics". He obtained his Ph.D. from Cornell University in 2003, under the supervision of José F. Escobar (thesis: *Existence and Compactness Theorems on Conformal Deformation of Metrics*).

Despite the usual path being to go for a postdoctoral research, Codá Marques had in mind that his mission was to return to Brazil. The Instituto Nacional de Matemática Pura e Aplicada (IMPA) had already offered him a position of researcher, and he accepted it. But after six months in Brazil, Escobar, who was his main connection with researchers outside of Brazil, died. Codá Marques faced the difficulties of doing research in isolation, so he decided to accept an invitation to stay one year as a postdoc at Stanford University. There he was influenced by Richard Schoen's school of thought in geometry and met André Neves (who would become his main collaborator), and many other of his contacts.

He worked at the IMPA from 2003 to 2014.

Codá Marques and Neves "Min-max theory and the Willmore conjecture" was uploaded to arXiv on February 2012, in it they solved the Willmore conjecture, using Almgren–Pitts min-max theory, which was then "a relatively old tool and already somewhat out of favor". According to Harold Rosenberg, using this tool was possible because the pair discovered a connection between objects that were apparently very different: "connecting the problem with questions about minimal surfaces on the sphere [...] a priori there would be no reason for these things to be connected. It's curious, very curious."

On September 1, 2014, Codá Marques joined Princeton University as a full professor.

## Work

Some of his best known works are the following:

- February 2012: In cooperation with André Neves, the solution to the Willmore conjecture (Willmore, 1965)
- May 2012: In cooperation with Ian Agol and André Neves, the solution to the Freedman–He–Wang conjecture (Freedman–He–Wang, 1994)
- April 2010: In cooperation with Simon Brendle and André Neves, a counter-example to the rigidity conjecture of Min-Oo

Work on Yau's conjecture (Yau, 1982) that states that any compact tri-dimensional manifold has infinitely many smooth, closed, immersed minimal surfaces.

Codá Marques is currently working to extend Almgren–Pitts min-max theory.

## Honours

He was an invited speaker at the International Congress of Mathematicians (ICM) of 2010 in Hyderabad (on “Scalar curvature, conformal geometry, and the Ricci flow with surgery”), and a plenary speaker at the ICM of 2014 in Seoul (on “Minimal surfaces – variational theory and applications”).

He received the TWAS Prize in 2012.

He was awarded the ICTP Ramanujan Prize in 2012.

In 2014 he gave the Łojasiewicz Lecture (on "The min-max theory of minimal surfaces and applications") at the Jagiellonian University in Kraków.

He is a titular member of the Brazilian Academy of Sciences since 2014.

He shared the 2016 Oswald Veblen Prize in Geometry with André Neves.

## Personal life

He is married to mathematician Ana Maria Menezes de Jesus. She was a student of Harold Rosenberg at IMPA, and is currently an instructor of mathematics at Princeton University. Codá Marques and Menezes have a son named Pedro.