Fernando Codá Marques

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.

Fernando Codá Marques
Born (1979-10-08) 8 October 1979
São Carlos, Brazil
NationalityBrazilian
Alma materCornell University (Ph.D.)
IMPA (M.S.)
UFAL (B.S.)
Known forWillmore conjecture
Freedman–He–Wang conjecture
Min-Oo conjecture
Yau's conjecture
Contributions to Almgren–Pitts min-max theory
Yamabe problem
Equidistribution of minimal hypersurfaces
SpouseAna Maria Menezes
Children2
AwardsFermat Prize (2021)
Veblen Prize in Geometry (2016)
ICTP Ramanujan Prize (2012)
TWAS Prize (2012)
Scientific career
FieldsMathematics: geometric analysis, geometric topology
InstitutionsPrinceton University
IMPA
ThesisExistence and Compactness Theorems on Conformal Deformation of Metrics (2003)
Doctoral advisorJosé F. Escobar
Notable studentsAntoine Song
Websitehttps://www.math.princeton.edu/directory/fernando-coda-marques

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.[1][2]

Codá Marques started as a student of civil engineering at the Federal University of Alagoas in 1996, but switched to mathematics after two years.[3][4]

He obtained 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.[5]

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.[6]

In 2001, Codá Marques was awarded Cornell's Battig Prize for graduate students, for "excellence and promise in mathematics".[7] 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).[8]

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. 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.[6]

He worked at IMPA from 2003 to 2014.[9] On 1 September 2014, Codá Marques joined Princeton University as a full professor.[10]

Antoine Song was a student of his.[11]

Mathematical work

Some of his best known works are the following:[9][12]

Yamabe problem

In 2009, together with Richard Schoen and Marcus Khuri he did important work on the Yamabe problem.[13][14] 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,[15] 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 in 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.",[6][16] the solution to the Willmore conjecture[17] (Willmore, 1965)

Freedman–He–Wang conjecture

In May 2012, in cooperation with Ian Agol and André Neves,[18] Marques provided the solution to the Freedman–He–Wang conjecture (Freedman–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.[19]

Almgren–Pitts min-max theory

Codá Marques and André Neves are currently working to extend Almgren–Pitts min-max theory.[20]

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"),[21] and a plenary speaker at the ICM of 2014 in Seoul (on "Minimal surfaces – variational theory and applications").[22]

He received the TWAS Prize in 2012.[23]

He was awarded the ICTP Ramanujan Prize in 2012, "in recognition of his several outstanding contributions to differential geometry".[17][24]

In 2014 he gave the Łojasiewicz Lecture (on "The min-max theory of minimal surfaces and applications") at the Jagiellonian University in Kraków.[25]

He is a full member of the Brazilian Academy of Sciences since 2014.[1]

He shared the 2016 Oswald Veblen Prize in Geometry with André Neves, "for their remarkable work on variational problems in differential geometry [including] the proof of the Willmore conjecture.".[9][26]

He was elected to the 2018 class of fellows of the American Mathematical Society.[27]

He is a distinguished visiting professor of mathematics at the Institute for Advanced Study.[28]

He sits on the editorial board of the journal Annals of Mathematics.[29]

In 2020 he received a Simons Investigator Award.[30] 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, "for major advances obtained with André Neves on geometric applications of the calculus of variations".[31]

In 2023 he received the Frontiers of Science Award.[32]

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.[33][34] Codá Marques and Menezes have a son named Pedro and a daughter named Luisa.[35][36]

References
  1. "Academia Brasileira de Ciências". 6 October 2014. Archived from the original on 6 October 2014. Retrieved 17 December 2021.
  2. "Alagoano é destaque no Brasil e no exterior" Archived 8 August 2014 at the Wayback Machine. culturadigital.br (in Portuguese). Retrieved on 11 May 2016.
  3. "Rede Globo > entrevistas – Fernando Codá relata os desafios da rotina de trabalho de um matemático". redeglobo.globo.com (in Portuguese). Retrieved on 11 May 2016.
  4. Revista Turismo e Negócios – "Entrevista: Pesquisador alagoano é destaque internacional Archived 30 July 2018 at the Wayback Machine" (2011, in Portuguese)
  5. "Alagoas vira referência em formação de matemáticos no País".
  6. João Moreira Salles (December 2013), "Senhor dos anéis: Um grande resultado matemático e as suas consequências", Revista Piauí (in Portuguese), archived from the original on 8 September 2014
  7. "Department Prizes and Awards for Graduate Students". cornell.edu. Retrieved on 11 May 2016.
  8. Fernando Codá Marques at the Mathematics Genealogy Project
  9. Kehoe, Elaine (April 2016), "2016 Oswald Veblen Prize in Geometry" (PDF), Notices of the AMS, 63 (4): 429–431, doi:10.1090/noti1358
  10. "Princeton University – Board approves three faculty appointments". princeton.edu. Retrieved on 11 May 2016.
  11. Fernando Codá Marques at the Mathematics Genealogy Project
  12. Web-site of the Institute of Mathematics of the Jagiellonian University > Research > Łojasiewicz Lecture > Past lectures > 2014 Lecture > Fernando Coda Marques Retrieved on 20 May 2016.
  13. Khuri, M. A., Marques, F. C., & Schoen, R. M. (2009). A compactness theorem for the Yamabe problem. Journal of Differential Geometry, 81(1), 143–196.
  14. Marques, F. C. (2005). A priori estimates for the Yamabe problem in the non-locally conformally flat case. Journal of Differential Geometry, 71(2), 315–346.
  15. Brendle, Simon; Marques, Fernando C.; Neves, Andre (8 December 2010). "Deformations of the hemisphere that increase scalar curvature". Inventiones Mathematicae. 185 (1): 175–197. arXiv:1004.3088. Bibcode:2011InMat.185..175B. doi:10.1007/s00222-010-0305-4. ISSN 0020-9910. S2CID 73530161.
  16. Marques, Fernando; Neves, André (1 January 2014). "Min-Max theory and the Willmore conjecture". Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6. S2CID 50742102.
  17. "News: Brazilian mathematician named Ramanujan Prize winner" Archived 11 August 2014 at the Wayback Machine. abelprize.no. Retrieved on 11 May 2016.
  18. Agol, Ian; Marques, Fernando; Neves, André (1 January 2015). "Min-max theory and the energy of links". Journal of the American Mathematical Society. 29 (2): 561–578. arXiv:1205.0825. doi:10.1090/jams/835. ISSN 0894-0347. S2CID 85524512.
  19. Brendle, S.; Marques, F. C.; Neves, A. (2017). "Density of minimal hypersurfaces for generic metrics". arXiv:1710.10752 [math.DG].
  20. "Interview with Fernando Codá Marques" (PDF), Notices of the AMS, 63 (2): 142–143, February 2016, doi:10.1090/noti1344.
  21. International Mathematical Union (IMU) . "ICM Plenary and Invited Speakers since 1897" Archived 24 November 2017 at the Wayback Machine. mathunion.org. Retrieved on 16 May 2016.
  22. "Seoul ICM 2014 – Schedule of Plenary Lectures". Archived from the original on 16 July 2015. Retrieved 17 December 2021.
  23. "Prizes and Awards". The World Academy of Sciences. 2016.
  24. Kehoe, Elaine (February 2013), "Codá Marques Awarded Ramanujan and TWAS Prizes" (PDF), Mathematics People, Notices of the AMS, 60 (2): 245.
  25. "Fernando Coda Marques – Institute of Mathematics of the Jagiellonian University". www.im.uj.edu.pl. Retrieved 29 December 2016.
  26. "News, Events and Announcements". American Mathematical Society. Retrieved on 11 May 2016.
  27. 2018 Class of the Fellows of the AMS, American Mathematical Society, retrieved 3 November 2017
  28. "Fernando Coda Marques". 9 December 2019.
  29. https://annals.math.princeton.edu/
  30. "Mathematician Codá Marques named 2020 Simons Investigator". Princeton University. Retrieved 17 December 2021.
  31. "Institut de Mathématiques de Toulouse – Fermat Prize 2021". www.math.univ-toulouse.fr. Archived from the original on 14 December 2021. Retrieved 17 December 2021.
  32. "The First International Congress of Basic Science (ICBS)".
  33. Paulo Rolemberg (2013) – "Filha de agricultores, sergipana de 26 anos fará pós-doutorado na França". UOL Educação. Retrieved on 11 May 2016.
  34. "Ana Menezes". princeton.edu. Retrieved on 11 May 2016.
  35. "Joint Mathematics Meeting, Seattle, AMS, MAA, "Prizes and Awards", 2016" (PDF). Retrieved 17 December 2021.
  36. https://www.ams.org/journals/notices/202009/rnoti-p1406.pdf

Further reading
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