Fernando Codá dos Santos Cavalcanti Marques (born in 1979) is a Brazilian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

working mainly in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s and

Morse theory In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differenti ...

. He is a professor at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

. In 2012, together with André Neves, he proved the Willmore conjecture. Since then, among proving other important conjectures, Marques and Neves greatly extended

Almgren–Pitts min-max theory In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) is an analogue of Morse theory for hypersurfaces. The theory started with the efforts for generalizing George David Birkhoff's m ...

to prove theorems about minimal surfaces.

Early years, education and career

Codá Marques was born on 8 October 1979 in

São Carlos São Carlos (Saint Charles, in English, ; named after Charles Borromeo, Saint Charles Borromeo) is a Brazilian city and municipality in the Interior of São Paulo, interior of the state of São Paulo, 254 kilometers from the city of São Paulo. ...

and grew up in

Maceió Maceió (), formerly anglicised as Maceio, is the capital and the largest city of the coastal state of Alagoas, Brazil. The name "Maceió" is an Indigenous term for a Spring (hydrology), spring. Most maceiós flow to the sea, but some get trapped ...

. His parents were both professors of

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

."Alagoano é destaque no Brasil e no exterior"
. ''culturadigital.br'' (in Portuguese). Retrieved 11 May 2016. Codá Marques started as a student of

civil engineering Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...

at the Federal University of Alagoas in 1996, but switched to mathematics after two years. He earned a master's degree from the Instituto Nacional de Matemática Pura e Aplicada (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 Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

to learn

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of ...

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, Marques had in mind that his mission was to return to Brazil. 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 Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

. 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. Codá Marques worked at IMPA from 2003 to 2014. On 1 September 2014, Codá Marques joined

as a full professor. One of his PhD students at Princeton was Antoine Song.

Mathematical work

Some of his best known works are the following:

Yamabe problem

In 2009, together with Richard Schoen and Marcus Khuri he did important work on the Yamabe problem. He solved Schoen's conjecture on compactness in the Yamabe problem for spin manifolds.

Rigidity conjecture of Min-Oo

In April 2010, in cooperation with Simon Brendle and André Neves, Marques provided a counter-example to the rigidity conjecture of Min-Oo.

Willmore conjecture

Codá Marques and Neves "Min-max theory and the Willmore conjecture" was uploaded to

arXiv arXiv (pronounced as "archive"—the X represents the Chi (letter), Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not Scholarly pee ...

in February 2012, in it they solved the Willmore conjecture, using

, 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.", the solution to the Willmore conjecture ( Willmore, 1965)

Freedman–He–Wang conjecture

In May 2012, in cooperation with Ian Agol and André Neves, Marques provided the solution to the Freedman–He–Wang conjecture (

Freedman A freedman or freedwoman is a person who has been released from slavery, usually by legal means. Historically, slaves were freed by manumission (granted freedom by their owners), emancipation (granted freedom as part of a larger group), or self- ...

–He–Wang, 1994)

Yau's conjecture

In December 2017, in cooperation with Kei Irie and André Neves, he solved Yau's conjecture ( Yau, 1982) in the generic case.

Almgren–Pitts min-max theory

Codá Marques and André Neves are currently working to extend

Honours

Codá Marques was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

(ICM) of 2010 in

Hyderabad Hyderabad is the capital and largest city of the Indian state of Telangana. It occupies on the Deccan Plateau along the banks of the Musi River (India), Musi River, in the northern part of Southern India. With an average altitude of , much ...

(on "

Scalar curvature In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry ...

conformal geometry In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two di ...

, and the Ricci flow with surgery"), and a plenary speaker at the ICM of 2014 in

Seoul Seoul, officially Seoul Special Metropolitan City, is the capital city, capital and largest city of South Korea. The broader Seoul Metropolitan Area, encompassing Seoul, Gyeonggi Province and Incheon, emerged as the world's List of cities b ...

(on " Minimal surfaces – variational theory and applications"). Codá Marques received the

TWAS Prize This is a list of recipients of the TWAS Prize, awarded annually by The World Academy of Sciences (TWAS) since 1985. Summary Agricultural Sciences Biology Chemistry Earth Sciences Engineering Sciences Mathematics ...

in 2012. Codá Marques was awarded the ICTP Ramanujan Prize in 2012, "in recognition of his several outstanding contributions to differential geometry"."News: Brazilian mathematician named Ramanujan Prize winner"
. abelprize.no. Retrieved 11 May 2016. 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 full member of the

Brazilian Academy of Sciences Brazilian commonly refers to: * Brazil, a country * Brazilians, its people * Brazilian Portuguese, its dialect Brazilian may also refer to: * "The Brazilian", a 1986 instrumental music piece by Genesis * Brazilian Café, Baghdad, Iraq (1937) * Bra ...

since 2014. Codá Marques shared the 2016 Oswald Veblen Prize in Geometry with André Neves, "for their remarkable work on variational problems in differential geometry ncludingthe proof of the Willmore conjecture.". He was elected to the 2018 class of

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Codá Marques is a distinguished visiting professor of mathematics at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. He sits on the editorial board of the journal ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

''. In 2020, he received a Simons Investigator Award. The citation reads: "His recent work, in collaboration with André Neves, developed a full Morse theory for the area functional in closed

Riemannian manifold In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the N-sphere, n-sphere, hyperbolic space, and smooth surf ...

s. The ideas introduced by them have revitalized the subject, leading to the discovery that closed minimal surfaces are ubiquitous in these spaces." In 2021, he was awarded the Fermat Prize, "for major advances obtained with André Neves on geometric applications of the calculus of variations". In 2023, he received the ''Frontiers of Science Award''.

Personal life

He is married to mathematician Ana Maria Menezes de Jesus. She was a student of Harold Rosenberg at IMPA, and is currently a research scholar of mathematics at

. Codá Marques and Menezes have two children, a son and a daughter.News: Mathematics People
''

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...

'', Volume 67, Number 9, p. 1407, 2020

References

External links

Interview with Fernando Codá Marques, 2011

Academia Brasileira de Ciências – Fernando Codá dos Santos Cavalcanti Marques
(in Portuguese)
Interview to Alagoas 24 Horas
(in Portuguese)

(in Portuguese)
CNPq – Jovem matemático é destaque no Brasil e no exterior
(in Portuguese)
Academia Brasileira de Ciências – Especial: Membros Afiliados da ABC do Rio de Janeiro 2009
(in Portuguese) * * Fernando Codá Marques' lecture
Soap films in mathematics
(video from 2014) * Fernando Codá Marques' lecture
Gometria e Análise
(video from 2010, in Portuguese) {{DEFAULTSORT:Codá Marques, Fernando 21st-century Brazilian mathematicians 1979 births Living people Cornell University alumni Princeton University faculty Differential geometers Members of the Brazilian Academy of Sciences People from São Carlos Partial differential equation theorists Topologists Instituto Nacional de Matemática Pura e Aplicada alumni Instituto Nacional de Matemática Pura e Aplicada researchers Brazilian expatriate academics in the United States Institute for Advanced Study visiting scholars TWAS laureates Fellows of the American Mathematical Society