Yves Benoist

File:Yves Benoist.jpg 2018]]

Yves Benoist is a French mathematician, known for his work on group dynamics on homogeneous spaces. He is currently a Senior Researcher (Directeur de Recherche) of CNRS at the University of Paris-Sud.

In 1990 Benoist proved a longstanding open conjecture with Patrick Foulon and François Labourie about Anosov flows on compact, negatively curved manifolds.Y. Benoist, P. Foulon, F. Labourie: Flots d'Anosov à distributions stable et instable différentiables. J. Amer. Math. Soc. 5 (1992), no. 1, 33–74. In the 2000s he wrote a series of papers on the divisible convex sets in projective space and periodic tilings by such sets.

In 2011 he was awarded the Clay Research Award along with his former doctoral student, Jean-François Quint.[http://www.claymath.org/research Clay Research Award] The prize citation highlighted their work on stationary measures and closed orbits for non-abelian group actions on homogeneous spaces, solving a long-standing conjecture of Hillel Furstenberg. They showed that in homogeneous spaces of finite volume, orbits of a Zariski dense subgroup of a semisimple group equidistribute towards algebraic measures.

He gave the 2012 Takagi Lectures[http://www.ms.u-tokyo.ac.jp/~toshi/jjm/JJM_HP/contents/takagi/10th/index.htm 10th Takagi Lectures] in Kyoto at the Research Institute for Mathematical Sciences (RIMS). In 2014 he was an Invited speaker at the International Congress of Mathematicians in Seoul.

Selected works

{{cite journal | last1=Benoist | first1=Yves | last2=Quint | first2=Jean-François | title=Mesures stationnaires et fermés invariants des espaces homogènes II | journal=Comptes Rendus Mathematique | publisher=Elsevier BV | volume=349 | issue=5–6 | year=2011 | issn=1631-073X | doi=10.1016/j.crma.2011.01.015 | pages=341–345 | url=http://www.numdam.org/articles/10.1016/j.crma.2011.01.015/ | language=fr}}
{{cite journal | last1=Benoist | first1=Yves | last2=Quint | first2=Jean-Francois | title=Random walks on finite volume homogeneous spaces | journal=Inventiones Mathematicae | publisher=Springer Science and Business Media LLC | volume=187 | issue=1 | date=29 March 2011 | issn=0020-9910 | doi=10.1007/s00222-011-0328-5 | pages=37–59| s2cid=253741706 }}
{{cite journal | last=Benoist | first=Yves | title=Convexes divisibles | journal=Comptes Rendus de l'Académie des Sciences - Series I - Mathematics | publisher=Elsevier BV | volume=332 | issue=5 | year=2001 | issn=0764-4442 | doi=10.1016/s0764-4442(01)01878-x | pages=387–390 | language=fr}}
{{cite journal | last=Benoist | first=Yves | title=Convexes divisibles II | journal=Duke Mathematical Journal | publisher=Duke University Press | volume=120 | issue=1 | date=1 October 2003 | issn=0012-7094 | doi=10.1215/s0012-7094-03-12014-1}}
{{cite journal | last=Benoist | first=Yves | title=Convexes divisibles III | journal=Annales Scientifiques de l'École Normale Supérieure | publisher=Societe Mathematique de France | volume=38 | issue=5 | year=2005 | issn=0012-9593 | doi=10.1016/j.ansens.2005.07.004 | pages=793–832}}
{{cite journal | last=Benoist | first=Yves | title=Convexes divisibles IV : Structure du bord en dimension 3 | journal=Inventiones Mathematicae | publisher=Springer Science and Business Media LLC | volume=164 | issue=2 | date=9 January 2006 | issn=0020-9910 | doi=10.1007/s00222-005-0478-4 | pages=249–278 | s2cid=123470471 | language=fr}}
{{cite journal | last=Benoist | first=Y. | title=Propriétés Asymptotiques des Groupes Linéaires | journal=Geometric and Functional Analysis | publisher=Springer Science and Business Media LLC | volume=7 | issue=1 | year=1997 | issn=1016-443X | doi=10.1007/pl00001613 | pages=1–47| s2cid=126085434 }}
{{cite journal | last=Benoist | first=Yves | title=Actions Propres sur les Espaces Homogenes Reductifs | journal=The Annals of Mathematics | publisher=JSTOR | volume=144 | issue=2 | year=1996 | pages=315–347 | issn=0003-486X | doi=10.2307/2118594 | jstor=2118594 }}
{{cite journal | last1=Benoist | first1=Yves | last2=Foulon | first2=Patrick | last3=Labourie | first3=François | title=Flots d'Anosov à distributions stable et instable différentiables | journal=Journal of the American Mathematical Society | publisher=American Mathematical Society (AMS) | volume=5 | issue=1 | year=1992 | issn=0894-0347 | doi=10.1090/s0894-0347-1992-1124979-1 | pages=33–74| doi-access=free }}

Lecture notes on Yves Benoist's work

Jean-François Quint: Convexes divisibles, d'après Yves Benoist. Séminaire Bourbaki, June 2008.
François Ledrappier: Mesures sur les espaces station aires homogeneous, d'après Yves Benoist et Jean-François Quint Séminaire Bourbaki, 2012.

References

Category:20th-century French mathematicians

Category:Dynamical systems theorists

Category:Year of birth missing (living people)

Category:Living people

Category:21st-century French mathematicians