IHES Annual Report 2020 | 23

Fanny KASSEL Mathematics, CNRS research director.

FANNY KASSEL continued her work on actions of discrete groups on homogeneous spaces and geometric structures on manifolds. In particular she explored analogues, in higher rank, of the classical notion of convex cocompact group in rank one. In this framework, with Jeffrey Danciger, François Guéritaud, Gye-Seon Lee and Ludovic Marquis, she described all linear reflection groups à la Vinberg which are convex cocompact in real projective space. With Rafael Potrie, she investigated some more dynamical aspects and established links between discrete sub(semi)groups of Lie groups and hyperbolicity properties of cocycles. With Jean-Philippe Burelle and

Virginie Charette, she constructed fundamental domains for Anosov representations of free groups. With Toshiyuki Kobayashi, she investigated the spectrum of the Laplacian on certain pseudo-Riemannian locally homogeneous spaces.

SCIENTIFIC ACTIVITY

DISTINCTIONS

CNRS Bronze Medal (2015) ERC Starting Grant "Discrete Groups and Geometric Structures" (DiGGeS) (2016) Invited Speaker ICM (2018)

Editor of: Publications Mathématiques de l'IHES Astérisque Annales Mathématiques Blaise Pascal Journal of Lie Theory Geometriae Dedicata Gazette des Mathématiciens (Société Mathématique de France)

CONFERENCES

France Seminar « Raconte moi... », École normale supérieure, Paris (4 November) Raconte moi les représentations d'Anosov (video seminar)

United States Mini Course, Mathematical Sciences Research Institute, Berkeley (8 9 11 September) Anosov representations (video mini course)

PUBLICATIONS

With J. Danciger and F. Guéritaud Proper Affine Actions for Right angled Coxeter Groups Duke Math. J. 169 (2020), 2231-2280.

With J. Danciger, F. Guéritaud, G.-S. Lee and L. Marquis Convex Cocompactness for Coxeter Groups Pre-publication arXiv:2102.02757.

With T. Kobayashi Spectral Analysis on Pseudo Riemannian Locally Symmetric Spaces Proc. Japan Acad. Ser A. Math. Sci. 96 (2020), 69-74.

With R. Potrie Eigenvalue Gaps for Hyperbolic Groups and Semigroups Pre-publication arXiv:2002.07015.