Fernando Codá dos Santos Cavalcanti Marques (born 8 October 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, structure, space, models, and change. History On ...

working mainly in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

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 differentiabl ...

. He is a professor at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. In 2012, together with

André Neves André da Silva Graça Arroja Neves (born 1975, Lisbon) is a Portuguese mathematician and a professor at the University of Chicago. He joined the faculty of the University of Chicago in 2016. In 2012, jointly with Fernando Codá Marques, he sol ...

, he proved the

Willmore conjecture In differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was ...

Biography

Fernando Codá Marques was born on 8 October 1979 in

São Carlos São Carlos (Saint Charles, in English, ; named after Saint Charles Borromeo) is a Brazilian municipality in the interior of the state of São Paulo, 254 kilometers from the city of São Paulo. With a population of 254,484 inhabitants, it is th ...

and grew up in

Maceió Maceió (), formerly sometimes 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. Most maceiós flow to the sea, but some get trapped and form la ...

. His parents were both professors of

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

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

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...

at the

Federal University of Alagoas Located in the city of Maceió, the Federal University of Alagoas ( pt, Universidade Federal de Alagoas, UFAL or Ufal) is the major university in coastal state Alagoas and one of the main research centers in Brazilian north eastern region (one o ...

in 1996, but switched to mathematics after two years. He obtained a master's degree from the

Instituto Nacional de Matemática Pura e Aplicada The Instituto Nacional de Matemática Pura e Aplicada (IMPA; en, National Institute for Pure and Applied Mathematics) is widely considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is loc ...

(IMPA) in 1999. Among his teachers at the IMPA were

Manfredo do Carmo Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil. Education and career Do Car ...

and

Elon Lages Lima Elon Lages Lima (July 9, 1929 – May 7, 2017) was a Brazilian mathematician whose research concerned differential topology, algebraic topology, and differential geometry. Lima was an influential figure in the development of mathematics in Brazil. ...

. Following the advice of Manfredo do Carmo, Codá Marques went to

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

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 l ...

from

José F. Escobar José Fernando "Chepe" Escobar (born 20 December 1954, in Manizales, Colombia) was a Colombian mathematician known for his work on differential geometry and partial differential equations. He was professor at Cornell University. He completed hi ...

, 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. 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 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 ...

. There he was influenced by

Richard Schoen Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984. Career Born in Celina, Ohio, and a ...

's school of thought in geometry and met

(who would become his main collaborator), and many other of his contacts. He worked at IMPA from 2003 to 2014. On 1 September 2014, Codá Marques joined

as a full professor. Antoine Song was a student of his.

Mathematical work

Some of his best known works are the following:

Yamabe problem

In 2009, together with

and Marcus Khuri he did important work on the

Yamabe problem The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: By computing a formula for how the scalar curvatur ...

. He solved Schoen's conjecture on compactness in the Yamabe problem for

spin manifold In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical ...

Rigidity conjecture of Min-Oo

In April 2010, in cooperation with

Simon Brendle Simon Brendle (born June 1981) is a German mathematician working in differential geometry and nonlinear partial differential equations. He received his Dr. rer. nat. from Tübingen University under the supervision of Gerhard Huisken (2001). He ...

and

, Marques provided a

counter-example A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is ...

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 "archive"—the X represents the 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 peer review. It consists of ...

in February 2012, in it they solved the

, using

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 ...

, which was then "a relatively old tool and already somewhat out of favor". According to

Harold Rosenberg Harold Rosenberg (February 2, 1906 – July 11, 1978) was an American writer, educator, philosopher and art critic. He coined the term Action Painting in 1952 for what was later to be known as abstract expressionism. Rosenberg is best known for ...

, 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 Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Education and career Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and ...

and André Neves, Marques provided the solution to the Freedman–He–Wang conjecture (

Freedman A freedman or freedwoman is a formerly enslaved person who has been released from slavery, usually by legal means. Historically, enslaved people were freed by manumission (granted freedom by their captor-owners), emancipation (granted freedom a ...

–He–Wang, 1994)

Yau's conjecture

In December 2017, in cooperation with Kei Irie and André Neves, he solved

Yau's conjecture In differential geometry, Yau's conjecture from 1982, is a mathematical conjecture which states that a closed Riemannian 3-manifold has an infinite number of smooth closed immersed minimal surfaces. It is named after Shing-Tung Yau. It was the ...

( Yau, 1982) in the

generic Generic or generics may refer to: In business * Generic term, a common name used for a range or class of similar things not protected by trademark * Generic brand, a brand for a product that does not have an associated brand or trademark, other ...

case.

Almgren–Pitts min-max theory

Codá Marques and André Neves are currently working to extend

Honours

He was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

(ICM) of 2010 in

Hyderabad Hyderabad ( ; , ) is the capital and largest city of the Indian state of Telangana and the ''de jure'' capital of Andhra Pradesh. It occupies on the Deccan Plateau along the banks of the Musi River (India), Musi River, in the northern part ...

(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 d ...

, and the

Ricci flow with surgery Ricci () is an Italian surname, derived from the adjective "riccio", meaning curly. Notable Riccis Arts and entertainment * Antonio Ricci (painter) (c.1565–c.1635), Spanish Baroque painter of Italian origin * Christina Ricci (born 1980), Ameri ...

"), and a plenary speaker at the ICM of 2014 in

Seoul Seoul (; ; ), officially known as the Seoul Special City, is the capital and largest metropolis of South Korea.Before 1972, Seoul was the ''de jure'' capital of the Democratic People's Republic of Korea (North Korea) as stated iArticle 103 ...

(on "

Minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

s – variational theory and applications"). He received the

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

in 2012. He was awarded the

ICTP Ramanujan Prize The DST-ICTP-IMU Ramanujan Prize for Young Mathematicians from Developing Countries is a mathematics prize awarded annually by the International Centre for Theoretical Physics in Italy. The prize is named after the Indian mathematician Srinivas ...

in 2012, "in recognition of his several outstanding contributions to differential geometry"."News: Brazilian mathematician named Ramanujan Prize winner"
. ''abelprize.no''. Retrieved on 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 The Brazilian Academy of Sciences ( pt, italic=yes, Academia Brasileira de Ciências or ''ABC'') is the national academy of Brazil. It is headquartered in the city of Rio de Janeiro and was founded on May 3, 1916. Publications It publishes a lar ...

since 2014. He shared the 2016

Oswald Veblen Prize in Geometry __NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen. The Veblen Prize is now worth US$5000, and is ...

with

, "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 concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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, ...

. He is a distinguished visiting professor of mathematics at the

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

. 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 the ...

''. In 2020 he received a

Simons Investigator Award The Simons Foundation is a private foundation established in 1994 by Marilyn and James Harris Simons, Jim Simons with offices in New York City. As one of the largest charitable organizations in the US with assets of over $5 billion in 2022, the ...

. The citation reads: "His recent work, in collaboration with André Neves, developed a full Morse theory for the area functional in closed Riemannian manifolds. 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 The Fermat prize of mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geometry * Numb ...

, "for major advances obtained with André Neves on geometric applications of the calculus of variations".

Personal life

He is married to mathematician Ana Maria Menezes de Jesus. She was a student of

at IMPA, and is currently an instructor of mathematics at Princeton University. Codá Marques and Menezes have a son named Pedro and a daughter named Luisa.https://www.ams.org/journals/notices/202009/rnoti-p1406.pdf

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:Coda 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 PDE 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