Serge Marc Cantat (born 3 June 1973, in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

) is a French mathematician, specializing in geometry and dynamical systems. Cantat received his PhD under the supervision of

Étienne Ghys Étienne Ghys (born 29 December 1954) is a French mathematician. His research focuses mainly on geometry and dynamical systems, though his mathematical interests are broad. He also expresses much interest in the historical development of mathema ...

in 1999 at the

École normale supérieure de Lyon The École normale supérieure de Lyon (also known as ENS de Lyon, ENSL or Normale Sup' Lyon) is a French grande école located in the city of Lyon. It is one of the four prestigious écoles normales supérieures in France. The school is ...

. Cantat is a directeur de recherche of CNRS at the Institut de recherches mathématiques de Rennes (

University of Rennes 1 The University of Rennes 1 is a public university located in the city of Rennes, France. It is under the Academy of Rennes. It specializes in science, technology, law, economics, management and philosophy. There are currently about students en ...

). He was previously directeur de recherche of CNRS at ENS Paris. His research deals with complex dynamics and dynamics of automorphisms of algebraic surfaces. He examined the algebraic structure of

Cremona group In algebraic geometry, the Cremona group, introduced by , is the group of birational automorphisms of the n-dimensional projective space over a field It is denoted by Cr(\mathbb^n(k)) or Bir(\mathbb^n(k)) or Cr_n(k). The Cremona group is natura ...

s (''i.e.'' groups of

birational In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational f ...

automorphisms of

n

-dimensional projective spaces over a field

k

) and showed with Stéphane Lamy that for an algebraically closed field

k

and for dimension

n

=2 the Cremona group

\mathrm(\mathbb^n(k))

is not a

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

. In particular, if

k

is the field of complex numbers and

n

=2, the Cremona group contains an infinite non-countable family of different normal subgroups. In 2018, Cantat was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro. In 2012 he received the

Prix Paul Doistau–Émile Blutet The Prix Paul Doistau–Émile Blutet is a biennial prize awarded by the French Academy of Sciences in the fields of mathematics and physical sciences since 1954. Each recipient receives 3000 euros. The prize is also awarded quadrennially in bio ...

for his work on dynamic systems (and especially holomorphic dynamic systems). In 2012 he was an invited speaker at the

European Congress of Mathematics The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM). The ECM are held every four years and are timed precisely betwe ...

Kraków Kraków (), or Cracow, is the second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city dates back to the seventh century. Kraków was the official capital of Poland until 1596 ...

. In 2012 he was awarded the Prix La Recherche.

Selected publications

* Dynamique des automorphismes des surfaces K3, Acta Math., Vol. 187, 2001, pp. 1–57. * with C. Favre: Symétries birationnelles des surfaces feuilletées, J. Reine Ange. Math., Vol. 561, 2003, pp. 199–235
Arxiv
* Endomorphismes des variétés homogènes, L'Enseignement Math., Vol. 49, 2004, pp. 237–262 * Difféomorphismes holomorphes Anosov, Commentarii Math. Helvetici, vol. 79, 2004, pp. 779–797 * with Frank Loray: Holomorphic dynamics, Painlevé VI equation, and character varieties, Annales de l'Institut Fourier, Vol. 59, 2009, pp. 2927–2978
Arxiv
* Bers and Hénon, Painlevé and Schroedinger, Duke Math. Journal, Vol. 149, 2009, pp. 411–460
Arxiv
* with Antoine Chambert-Loir, Vincent Guedj: Quelques aspects des systèmes dynamiques polynomiaux, Panorama et Synthèse, Volume 30, Société Math. de France 2010 ** In Cantat's introduction, the chapter '' Quelques aspects des systèmes dynamiques polynomiaux, existence, exemples, rigidité '', pp. 13–96, with Chambert-Loir: ''Dynamique p-adique (d'après les exposés de Jean-Christophe Yoccoz) '', p. 295
Arxiv
* with Abdelghani Zeghib: Holomorphic Actions, Kummer Examples, and Zimmer Program, Annales Scientifique de l'ENS, Vol. 45, 2012, pp. 447–489
Arxiv
* Sur les groupes de transformations birationnelles des surfaces, Annals of Math., Vol. 174, 2012, pp. 299–334 * with Igor Dolgachev: Rational Surfaces with a Large Group of Automorphisms, J. Amer. Math. Soc., Vol. 25, 2012, pp. 863–905
Arxiv

Dynamics of automorphisms of compact complex surfaces
in: Frontiers in Complex Dynamics: In celebration of John Milnor's 80th birthday, Princeton Mathematical Series, Princeton University Press, 2012, pp. 463–514 * with Stéphane Lamy: Normal subgroups of the Cremona group, Acta Mathematica, Vol. 210, 2013, pp. 31–94
Arxiv

References

External links

Homepage

Portrait at Espaces des Sciences

* * * * {{DEFAULTSORT:Cantat, Serge 20th-century French mathematicians 21st-century French mathematicians 1973 births Living people Prix Paul Doistau–Émile Blutet laureates