Artur Avila

{{Short description|Brazilian and French mathematician (born 1979)}}

{{Infobox scientist

| name = Artur Avila

| image = Artur Ávila (cropped).jpg

| image_size = 220px

| caption = Avila at the Mathematical Research Institute of Oberwolfach in 2012.

| birth_name = Artur Avila Cordeiro de Melo

| birth_date = {{Birth date and age|df=yes|1979|06|29}}

| birth_place = Rio de Janeiro, Brazil

| death_date =

| death_place =

| nationality = {{hlist|Brazil|France{{citation|url=http://www.math.jussieu.fr/~artur/cur.pdf|archive-url=https://web.archive.org/web/20140508115811/http://www.math.jussieu.fr/~artur/cur.pdf|archive-date=2014-05-08|title=Curriculum vitae}}}}

| fields = Mathematics

| workplaces = {{ubl|University of Zurich|CNRS|Paris Diderot University (Paris 7)|Instituto Nacional de Matemática Pura e Aplicada}}

| alma_mater = {{ubl|Instituto Nacional de Matemática Pura e Aplicada (PhD and MS) | Federal University of Rio de Janeiro (BS)}}

| thesis_title = Bifurcações de tranformações unimodais sob os pontos de vistas topológico e métrico

| thesis_year = 2001

| doctoral_advisor = Welington de Melo

| known_for = {{ubl|Dynamical systems|Spectral theory|Zorich–Kontsevich conjecture|Ten martini problem}}

| awards = {{ubl|Fields Medal (2014)|TWAS Prize (2013)|Michael Brin Prize in Dynamical Systems (2011)|EMS Prize (2008)|Salem Prize (2006)|Gold medal at the International Mathematical Olympiad (1995)}}

| doctoral_students =

}}

Artur Avila Cordeiro de Melo ({{IPA|pt|aʁˈtuʁ ˈavilɐ koʁˈde(j)ɾu d͡ʒi ˈmɛlu|lang}}; born 29 June 1979) is a Brazilian mathematician working primarily in the fields of dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal,{{cite news | url=https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/aug/13/fields-medals-2014-maths-avila-bhargava-hairer-mirzakhani | title=Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained | author=Alex Bellos | date= 13 August 2014 | newspaper=The Guardian| author-link=Alex Bellos }} being the first Latin American and lusophone to win such award. He has been a researcher at both the IMPA and the CNRS (working a half-year in each one). He has been a professor at the University of Zurich since September 2018.

Biography

At the age of 16, Avila won a gold medal at the 1995 International Mathematical Olympiad{{Cite web|url=http://www.imo-official.org/team_r.aspx?code=BRA&year=1995|title=International Mathematical Olympiad|website=www.imo-official.org|accessdate=4 September 2023}} and received a scholarship for the Instituto Nacional de Matemática Pura e Aplicada (IMPA) to start a M.S. degree while still attending high school in Colégio de São Bento and Colégio Santo Agostinho in Rio de Janeiro.{{Citation|last=Talarico |first=Bruna |title=Gênio da matemática carioca |date=16 January 2010 |work=O Dia Online |url=http://odia.terra.com.br/portal/rio/html/2010/1/genio_da_matematica_carioca_59005.html |language=pt |url-status=dead |archive-url=https://web.archive.org/web/20100122050606/http://odia.terra.com.br/portal/rio/html/2010/1/genio_da_matematica_carioca_59005.html |archive-date=22 January 2010 }} He completed his M.S. degree in 1997.{{cite web |last1=Pivetta |first1=Marcos |title=Artur Ávila: The man who calculates |url=https://revistapesquisa.fapesp.br/en/artur-avila-man-calculates/ |website=FAPESP |access-date=8 July 2022}} Later he enrolled in the Federal University of Rio de Janeiro (UFRJ), earning his B.S in mathematics.{{Citation|last=Moreira Salles |first=João |author-link=João Moreira Salles |title=Artur tem um problema |date=January 2010 |work=Piauí |url=http://revistapiaui.estadao.com.br/edicao-40/vultos-das-ciencias/artur-tem-um-problema |language=pt |url-status=dead |archive-url=https://web.archive.org/web/20150630063531/http://revistapiaui.estadao.com.br/edicao-40/vultos-das-ciencias/artur-tem-um-problema |archive-date=30 June 2015 |df=dmy }}

At the age of 19, Avila began writing his doctoral thesis on the theory of dynamical systems. In 2001 he finished it and received his PhD from IMPA. That same year he moved abroad to France to do postdoctoral research.{{cite web|url = http://g1.globo.com/educacao/noticia/2014/08/pesquisador-brasileiro-ganha-premio-equivalente-nobel-de-matematica.html|title= Pesquisador brasileiro ganha prêmio equivalente a 'Nobel' de matemática|date= 12 August 2014|author= Vanessa Fajardo|publisher=Grupo Globo|language=pt}} He works with one-dimensional dynamics and holomorphic functions.{{cite web|url=http://www.claymath.org/fas/research_fellows/Avila/|title=Artur Avila|publisher=Clay Mathematics Institute|access-date=12 July 2009|archive-date=18 May 2021|archive-url=https://web.archive.org/web/20210518102614/https://www.claymath.org/fas/research_fellows/Avila/|url-status=dead}} Since 2003 he has worked as a researcher for the Centre National de la Recherche Scientifique (CNRS) in France, later becoming a research director in 2008. His post-doctoral supervisor was Jean-Christophe Yoccoz.{{cite magazine | url=http://www.simonsfoundation.org/quanta/20140812-a-brazilian-wunderkind-who-calms-chaos/ | title=Brazilian Wunderkind Who Calms Chaos | magazine=Quanta Magazine | author1=Thomas Lin | author2=Erica Klarreich | date=12 August 2014}}

Mathematical work

Much of Artur Avila's work has been in the field of dynamical systems. In March 2005, at age 26, Avila and Svetlana Jitomirskaya proved the "conjecture of the ten martinis," a problem proposed by the American mathematical physicist Barry Simon.{{Cite web|date=2014-08-14|title=Press Release by the IMU regarding Artur Avila's mathematical work, on the occasion of his receipt of the Fields medal|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2014/news_release_avila2.pdf|access-date=2020-09-12|publisher=International Mathematical Union}} Mark Kac promised a reward of ten martinis to whoever solved the problem: whether or not the spectrum of a particular type of operator is a Cantor set, given certain conditions on its parameters. The problem had been unsolved for 25 years when Avila and Jitomirskaya answered it affirmatively.{{cite web|url=http://w3.impa.br/~avila/qmath.pdf|title= Solving the Ten Martini Problem|language=pt}}{{Cite book |arxiv = math/0503363|last1 = Avila|first1 = Artur|title = The Ten Martini Problem|volume = 690|pages = 5–16|last2 = Jitomirskaya|first2 = Svetlana|year = 2005|doi = 10.1007/3-540-34273-7_2|chapter = Solving the Ten Martini Problem|series = Lecture Notes in Physics|isbn = 978-3-540-31026-6|s2cid = 55259301}} Later that year, Avila and Marcelo Viana proved the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller flow on the moduli space of Abelian differentials on compact Riemann surfaces are all distinct.{{Cite arXiv |eprint = math/0508508|last1 = Avila|first1 = Artur|title = Simplicity of Lyapunov spectra: Proof of the Zorich-Kontsevich conjecture|last2 = Jitomirskaya|first2 = Svetlana|year = 2005}}{{cite journal |last1=Avila |first1=Artur |last2=Viana |first2=Marcelo |title=Dynamics in the moduli space of Abelian differentials |journal=Portugaliae Mathematica |volume=62 |issue=4 |year=2005 |pages=531–547 |url=https://www.emis.de/journals/PM/62f4/pm62f405.pdf |s2cid=9227819 }}

Honours and recognition

File:Four_Fields_medallists_plus_epsilon.jpg (at back), Maryam Mirzakhani, with Maryam's daughter Anahita) and Manjul Bhargava at the ICM 2014 in Seoul]]

Later, as a research mathematician, he received in 2006 a CNRS Bronze Medal as well as the Salem Prize, and was a Clay Research Fellow. He became the youngest professorial fellow (directeur de recherches) at the CNRS in 2008. The same year, he was awarded one of the ten prestigious European Mathematical Society prizes, and in 2009 he won the Grand Prix Jacques Herbrand from the French Academy of Sciences. In 2017 he gave the Łojasiewicz Lecture (on the "One-frequency Schrödinger operators and the almost reducibility conjecture") at the Jagiellonian University in Kraków.{{Cite web|url=http://www.im.uj.edu.pl/en_GB/lojasiewicz/2017|title=2017 Lecture - Institute of Mathematics of the Jagiellonian University|website=www.im.uj.edu.pl|language=en|access-date=2017-06-25}}

He was a plenary speaker at the International Congress of Mathematicians in 2010.{{cite web|title=ICM Plenary and Invited Speakers since 1897|url=http://www.mathunion.org/db/ICM/Speakers/SortedByCongress.php|publisher=International Congress of Mathematicians|access-date=14 August 2013|archive-date=8 November 2017|archive-url=https://web.archive.org/web/20171108012153/http://www.mathunion.org/db/ICM/Speakers/SortedByCongress.php|url-status=dead}}

In 2011, he was awarded the Michael Brin Prize in Dynamical Systems. He received the Early Career Award from the International Association of Mathematical Physics in 2012,{{Citation| title= The IAMP Early Career Award | url=http://www.iamp.org/page.php?page=page_award}} TWAS Prize in 2013{{Cite web |url=http://twas.org/article/twas-announces-2013-prize-winners |title=Prizes and Awards |date=2016 |publisher=The World Academy of Sciences}} and the Fields Medal in 2014.{{Citation| title= 2014 IMU Prize Winners| url= http://www.mathunion.org/general/prizes/2014/prize-citations/| access-date= 12 August 2014| archive-date= 11 November 2017| archive-url= https://web.archive.org/web/20171111174206/http://www.mathunion.org/general/prizes/2014/prize-citations| url-status= dead}}

He was elected a foreign associate of the US National Academy of Sciences in April 2019.{{cite web|url=http://www.nasonline.org/news-and-multimedia/news/2019-nas-election.html|title=2019 NAS Election|publisher=National Academy of Sciences|date=April 30, 2019}}

Avila is a member of World Minds.

=Diplomas, titles and awards=

1993: Gold medal at the Olimpíada Brasileira de Matemática, Brazil{{cite web|url=https://www.obm.org.br/2014/08/13/brasileiro-ganha-medalha-fields/|title=brasileiro-ganha-medalha-fields|publisher=OBM - Olimpíada Brasileira de Matemática|date=July 4, 2019}}
1994: Gold medal at the Olimpíada Brasileira de Matemática, Brazil
1995: Gold medal at the Olimpíada Brasileira de Matemática, Brazil
1995: Gold medal at the International Mathematical Olympiad, Canada{{cite web|url=https://www.imo-official.org/participant_r.aspx?id=3801|title=Artur Ávila Cordeiro de Melo|publisher=International Mathematical Olympiad|date=July 4, 2019}}
2001: PhD Thesis (advisor Welington de Melo){{cite web|url=https://impa.br/ensino/programas-de-formacao/doutorado/titulos-de-doutor-concedidos/graus-de-doutor-concedidos-em-2001/|title=Graus de Doutor concedidos em 2001

|publisher=IMPA|date=July 4, 2019}}

2005: Cours Peccot at the Collège de France
2006: Invited address at the ICMP
2006: Bronze medal of the CNRS
2006: Salem Prize
2008: Wolff Memorial Lectures, Caltech{{cite web|url=http://www.pma.caltech.edu/research-and-academics/mathematics/mathematics-seminars/thomas-wolff-memorial-lectures-in-mathematics|title=Thomas Wolff Memorial Lectures in Mathematics|publisher=Division of Physics, Mathematics and Astronomy (PMA) - Caltech|date=July 3, 2019}}
2008: Invited address at the European Congress of Mathematics{{cite web|url=https://www.sciencesmaths-paris.fr/en/%20http:/en/Researchers%20and%20Students-310.htm|title=The 5th European Congress of Mathematics|publisher=Fondation Sciences Mathématiques de Paris|date=July 3, 2019|access-date=4 July 2019|archive-date=4 July 2019|archive-url=https://web.archive.org/web/20190704173339/https://www.sciencesmaths-paris.fr/en/%2520http:/en/Researchers%2520and%2520Students-310.htm|url-status=dead}}
2008: European Mathematical Society Prize
2009: Grand Prix Jacques Herbrand of the French Academy of Sciences{{cite web|url=https://www.sciencesmaths-paris.fr/en/artur-avila-and-dynamics-370.htm|title=Artur Avila and Dynamics|publisher=Fondation Sciences Mathématiques de Paris|date=July 4, 2019|access-date=5 July 2019|archive-date=5 July 2019|archive-url=https://web.archive.org/web/20190705064654/https://www.sciencesmaths-paris.fr/en/artur-avila-and-dynamics-370.htm|url-status=dead}}
2010: Porter Lectures, Rice University{{cite web|url=http://smai.emath.fr/IMG/pdf_ICM-L1v3l.pdf|title=Un événement quadriennal : Le congrès international des mathématiciens|publisher=Société de Mathématiques Appliquées et Industrielles|date=July 3, 2019}}
2010: Plenary address at the International Congress of Mathematicians
2011: Blyth Lecture Series by the University of Toronto{{cite web|url=https://www.math.toronto.edu/cms/events/blyth-lecture-series/|title=Blyth Lecture Series|publisher=University of Toronto|date=July 3, 2019}}
2011: Michael Brin Prize in Dynamical Systems{{citation|url=https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/aug/13/fields-medals-2014-maths-avila-bhargava-hairer-mirzakhani|title=Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained|newspaper=The Guardian|date=August 13, 2014|first=Alex|last=Bellos|quote=Among his [Avila's] previous honors are ... the Michael Brin Prize (2011)}}.
2012: International Association of Mathematical Physics Early Career Award
2013: Prize of the Brazilian Mathematical Society{{cite web|url=https://www.sbm.org.br/en/premio-sbm|title=SBM Prize|publisher=Brazilian Mathematical Society|date=July 3, 2019}}
2013: TWAS Prize
2014: Bellow Lectures by the Northwestern University{{cite web|url=https://www.math.northwestern.edu/events/lectures/alexandra-bellow-distinguished-lecture-series.html|title=Bellow Lecture Series|publisher=Northwestern University|date=July 3, 2019|access-date=4 July 2019|archive-date=28 January 2021|archive-url=https://web.archive.org/web/20210128131044/https://www.math.northwestern.edu/events/lectures/alexandra-bellow-distinguished-lecture-series.html|url-status=dead}}
2014: Fields Medal
2015: TWAS-Lenovo Science Prize{{cite web|url=https://twas.org/opportunity/twas-lenovo-science-prize|title=TWAS-Lenovo Science Prize|publisher=The World Academy of Sciences (TWAS)|date=July 3, 2019}}
2017: Łojasiewicz Lecture by the Jagiellonian University: One-frequency Schrödinger operators and the almost reducibility conjecture

=Extra-academic distinctions=

2013: Member of the Brazilian Academy of Sciences{{cite web|url=http://agencia.fapesp.br/academia-brasileira-de-ciencias-empossa-novos-membros/17245/|title=Academia Brasileira de Ciências empossa novos membros|publisher=Agencia FAPESP|date=July 4, 2019}}
2015: Knight of the Legion of Honor{{cite web|url=https://es-us.noticias.yahoo.com/legión-honor-francia-enfermera-ébola-modiano-piketty-160115052.html|title=Legión de Honor en Francia para enfermera con ébola, Modiano y Piketty|publisher=YAHOO! Noticias|date=July 4, 2019}}
2019: Foreign associates of the National Academy of Sciences