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Bertrand EYNARD Mathematical Physics, CEA Research Director.
In 2021, BERTRAND EYNARD worked on establishing relations between Witten-Kontsevich intersection numbers , integrable systems, topological recursion and ribbon graphs combinatorics. In particular he proposed a compact rewriting of intersection numbers generating functions. With collaborators, he formulated r-spin intersection numbers in terms of ciliated ribbon graphs. With collaborators Elba Garcia-Failde, Olivier Marchal, and Nicolas Orantin, they proved the quantum curve conjecture for a wide class of curves. This conjecture claims that topological recursion computes the asymptotic expansion of flat sections of principal bundles
(GL(n) at the moment) over a Riemann surface endowed with meromorphic connection. This is a generalization of WKB asymptotic expansion.
SCIENTIFIC ACTIVITY
DISTINCTIONS
Invited Speaker ICM (2014) André Aisenstadt Chair, CRM, Montreal (2015) ERC Synergie "Recursive and Exact New Quantum Theory" (ReNewQuantum) (2018) Prix Mme Claude Berthault, Académie des sciences de Paris (2019)
Editor of: Random Matrices, Theory and Applications World Scientific Annales de l'Institut Henri Poincaré (D) Combinatorics, Physics and their interactions
CONFERENCES
Germany Noncommutative Geometry Meets Topological Recursion, University of Münster (August 16-20) Mixed Boundaries of the Ising Model on Random Maps (mini-courses)
Canada Mathematical Physics Seminar, Centre de recherches mathématiques Université de Montréal (December 7) Integrable System from an Algebraic Equation (seminar)
Italy School and Workshop on Topological Recursion, Otranto (September 6-17) Topological Recursion (conference)
South Korea Center for Geometry and Physics - Institute for Basic Science (IBS), Daejeon (September 6-17) Integrable System from an Algebraic Equation (seminar)
United Kingdom University of Birmingham (April 20-June 22) Geometry of Integrable Systems, Deformations and Generalized Cycles (conference)
PUBLICATIONS
With D. Lewanski and A. Ooms A Natural Basis for Intersection Numbers Prepublication arXiv:2108.00226.
With E. Garcia-Failde, O. Marchal and N. Orantin Quantization of Classical Spectral Curves via Topological Recursion Prepublication arXiv:2106.04339.
With R. Belliard, S. Charbonnier and E. Garcia-Failde Topological Recursion for Generalised Kontsevich Graphs and r spin Intersection Numbers Prepublication arXiv:2105.08035.
Fanny KASSEL Mathematics, CNRS Research Director.
FANNY KASSEL continued her work on actions of discrete groups on homogeneous spaces and geometric structures on manifolds. With Jeffrey Danciger, François Guéritaud, Gye-Seon Lee and Ludovic Marquis, she described all linear reflection groups (not necessarily Gromov hyperbolic) satisfying convex cocompactness properties in real projective space. With Rafael Potrie, she established links between discrete sub(semi)groups of Lie groups and hyperbolicity properties for cocycles in dynamics. With Nicolas Tholozan, she proved the Sharpness Conjecture for properly discontinuous and cocompact actions on reductive homogeneous spaces, which
allowed her to show that, in the corank-one case, these actions come from Anosov representations in the sense of Labourie. She prepared a Bourbaki Seminar lecture on surface groups in lattices of semisimple Lie groups.
SCIENTIFIC ACTIVITY
DISTINCTIONS
CNRS Bronze Medal (2015) ERC Starting Grant "Discrete Groups and Geometric Structures" (DiGGeS) (2016) ICM Invited Speaker (2018)
Editor of: Publications mathématiques de l'IHES Astérisque Annales Mathématiques Blaise Pascal Journal of Lie Theory Geometriae Dedicata Gazette de la Société Mathématique de France (2016-2020)
PUBLICATIONS
With J. Danciger, F. Guéritaud, G.-S. Lee and L. Marquis Convex Cocompactness for Coxeter Groups Prepublication arXiv:2102.02757.
With R. Potrie Eigenvalue Gaps for Hyperbolic Groups and Semigroups To appear in Journal of Modern Dynamics.
Groupes de surfaces dans les réseaux des groupes de Lie semi simples, d après J. Kahn, V. Marković, U. Hamenstädt, F. Labourie et S. Mozes Séminaire Bourbaki, talk no 1181, to appear in Astérisque.
CONFERENCES
France Séminaire virtuel francophone Groupes et Géométrie, séance mensuelle en partenariat avec le GDR Platon (June 3) Groupes de réflexions et géométrie projective convexe (video seminar)
Séminaire Bourbaki, Institut Henri Poincaré, Paris (October 2) Groupes de surfaces dans les réseaux des groupes de Lie semi simples (seminar)
Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Paris (October 15) Groupes de surfaces dans les réseaux des groupes de Lie semi simples (talk)
Colloquium, IMJ-PRG, Paris (November 25) Sous groupes discrets des groupes de Lie en rang supérieur (talk)
Germany Mini-Workshop: (Anosov)3, Institut de recherches mathématiques d'Oberwolfach (December 5-11) Mini Course on Anosov Representations (lecture)
United States Artin Groups, CAT(0) Geometry and Related Topics, a conference in honor of Ruth Charney, Université d'État de l'Ohio, Columbus (July 5-9) Convex Cocompactness and Coxeter Groups (video conference)
United Kingdom Geometry and Topology Seminar, University of Bristol (May 25) Convex Cocompactness and Coxeter Groups (video seminar)
