Nalini Anantharaman

Nalini Anantharaman, 8th from right, with arms crossed

Nalini Anantharaman (born February 26, 1976 ) is a French mathematician who deals with analysis and mathematical physics .

life and work

Anantharaman was at the 2000 University of Paris VI (Pierre et Marie Curie) at François Ledrappier doctorate . While working on her doctoral thesis, she was an assistant at the University of Paris VI, the University of Paris X and then at the École normal supérieure (ENS). In 2001 she became Maitre de conferences at the École normal supérieure de Lyon , where she qualified as a professor in 2006 . She then worked at the Center national de la recherche scientifique (CNRS) and Hadamard Assistant Professor at the École polytechnique (Center de Mathématiques Laurent Schwartz). Since 2009 she has been a professor at the University of Paris-South . In 2009 she was Miller Professor at the University of California, Berkeley .

In 2008 she was invited speaker at the European Congress of Mathematicians in Amsterdam ( Entropy and localization of eigenfunctions ) and in 2010 at the International Congress of Mathematicians in Hyderabad (India) ( A Hyperbolic dispersion estimate, with applications to the linear Schrödinger equation ).

She examined mathematical systems that serve as models for quantum chaos : the Laplace equation on compact surfaces of negative curvature . Here she achieved results regarding the QUE conjecture (Quantum Unique Ergodicity), which assumes a uniform distribution of the eigenfunctions of the Laplace operator in the semi-classical borderline case and was proven by Elon Lindenstrauss for the special case of arithmetic surfaces . For the general case, Anantharaman was able to show that semiclassically invariant measures of the eigenfunctions have a positive lower bound for the entropy .

Anantharaman has been Vice President of the Société Mathématique de France since 2012 and as such acts as co-editor of the Annales Scientifiques de l'ENS . In 2015 she was elected to the Academia Europaea .

Honors

• 2007 Prix ​​Gabrielle Sand and Marie Guido Trossi of the Académie des sciences
• 2010 Salem Prize
• 2011 Prix ​​Jacques Herbrand of the Académie des Sciences
• 2012 Henri Poincaré Prize
• 2018 plenary speaker at the ICM in Rio ( Delocalization of Schrödinger Eigenfunctions ).

Fonts

Essays

• Entropy and localization of self-functions . In: Annals of Mathematics , Vol. 168 (2008), pp. 435-475 ISSN  0003-486X
• with Stéphane Nonnenmacher and Herbert Koch : Entropy of Eigenfunctions . In: Vladas Sidoravičius (Ed.): New perspectives in mathematical physics. Selected contributions of the 15th International Congress on Mathematical Physics . Springer, Dordrecht 2009, ISBN 978-90-481-2809-9 , pp. 1–21.
• with Stéphane Nonnenmacher: Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold . In: Annales de l'Institut Fourier , Vol. 57 (2007), pp. 2465-2523 ISSN  0373-0956

Books

• Géodésiques fermées des surfaces, sous constraintes homologiques . Dissertation, University of Paris 2000.
• Entropy et localization des fonctions propres . Habilitation, ENS Lyon 2006.

Web links

• Homepage at the University of Paris-South