Fanny Kassel

Fanny Kassel is a distinguished French mathematician and CNRS Research Director at the Institute of Advanced Scientific Studies (IHES) since 2016, specializing in geometric group theory, discrete subgroups of Lie groups, and pseudo-Riemannian geometry. Her work has significantly advanced our understanding of geometric structures, dynamical systems, and spectral theory related to discrete group actions.

Education:

• Studied at Lycée Louis-le-Grand
• Entered École Normale Supérieure in 2003
• PhD from University of Paris Sud XI - Orsay in 2009 under Yves Benoist

Research Interests:

Fanny Kassel's research focuses on the geometric, dynamical and spectral aspects of discrete subgroups of Lie groups. She has made significant contributions to understanding flat Lorentzian manifolds of dimension 3, solving a conjecture by Drumm and Goldman from the early 1990s. Her work explores the actions of discrete groups on homogeneous spaces in connection with various geometric structures on manifolds (pseudo-Riemannian or projective) and higher-order Teichmüller-Thurston theory.

Her research bridges several mathematical disciplines, connecting representation theory with geometric structures and dynamical systems. She has particularly advanced our understanding of convex cocompactness in various geometric settings, including real projective geometry and pseudo-Riemannian hyperbolic spaces.

Research Trends:

Analysis of Kassel's most recent publications reveals a consistent focus on extending classical concepts of discrete group actions to broader geometric contexts. Her work increasingly explores connections between different geometric structures (projective, pseudo-Riemannian, hyperbolic) through the lens of discrete group actions. A notable trend is her development of "convex cocompactness" theory across multiple geometric settings, providing unifying frameworks for previously disconnected areas of research. Her collaborations, particularly with Danciger and Guéritaud, have been highly productive in advancing these interconnected research directions.

Awards and Recognition:

• CNRS Bronze Medal (2015)
• ERC Starting Grant (2016)
• ICM Rio Invited Lecturer (2018)
• Mathematics Medal of the French Academy of Sciences (2024)

Grants and Collaborations:

Kassel has led significant research projects including the ERC Starting Grant DiGGeS. She organizes the "Geometry and Discrete Groups" seminar at IHES and has organized numerous workshops and conferences. Her extensive collaborations include work with prominent mathematicians such as Jeffrey Danciger, François Guéritaud, Olivier Guichard, and Anna Wienhard. These collaborations have resulted in a rich body of work connecting geometric group theory with differential geometry and dynamical systems.

Research Environment:

Kassel works within the Alexander Grothendieck Laboratory at IHES, a premier research environment for mathematics and theoretical physics. She actively participates in the mathematical community through organizing seminars, workshops, and conferences. Her research group and collaborations form a vibrant network exploring the frontiers of geometric group theory and related fields.