Prix de l'Académie des sciences 2024: 6 winners in mathematics

CNRS Research Director Fanny Kassel of the Institut des hautes études scientifiques (IHES)1  has been awarded the Médaille de mathématiques by the Académie des Sciences. Fanny Kassel works at the intersection of geometry, group theory, Lie theory and dynamical systems. She studies discrete subgroups of Lie groups, particularly in higher rank, and their actions on various geometric spaces such as flag varieties or pseudo-Riemannian symmetric spaces.

Professor at the Laboratoire de Mathématiques de Versailles2 , Yvan Martel has been awarded the Prix Sophie Germain/Fondation de l'Institut de France (€8,000). Yves Martel studies nonlinear evolutionary partial differential equations, which are simplified forms of models introduced to describe wave propagation in physics. One of his main objectives is to establish wave stability properties with respect to perturbations. Yvan Martel also studies the appearance of singularities due to the nonlinear nature of these equations.

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CNRS Research Director at the Institut de Mathématiques de Toulouse3 , Mireille Capitaine has been awarded the Thérèse Gautier Prize (€3,500). Mireille Capitaine is particularly committed to developing the contribution of free probability theory to the study of the spectral properties of high-dimensional random matrices, notably via the subordination tool. She has also worked on the resolution of conjectures concerning large random matrices, which have important consequences for the theory of von Neumann algebras.

Lecturer at the Laboratoire de Mathématiques d'Orsay1 , Omar Mohsen has been awarded the Prix Jacques Herbrand/Fondation Mireille Cahn-Bunel by the Académie des Sciences (€8,000). Omar Mohsen is interested in partial differential equations and sub-Riemannian geometry, which he studies using methods from non-commutative geometry and operator algebras. In particular, he and his collaborators used C*-algebras of singular foliations to prove a conjecture of Helffer and Nourrigat concerning maximally hypoelliptic differential operators. In addition, he obtained a topological formula for their analytic index.

Professor at theAlexander Grothendieck Institute in Montpellier4 , Paul-Émile Paradana was awarded the Prix Joannidès/Fondation Joannidès by the Académie des Sciences (€2,500). Paul-Emile Paradan 's research lies at the interface between Atiyah-Singer index theory, representation theory and symplectic geometry. He has shown that the method of orbits applies to multiplicities of discrete series with respect to a reductive subgroup. He introduced a new class in equivariant cohomology that plays a crucial role in the index of transversely elliptic operators. With Michèle Vergne, they obtained a remarkable generalization of the theorem “quantization commutes with reduction” to the spinc frame. Recently, he obtained important convexity results in the description of projections of co-adjoint orbits of non-compact groups.

Professor at the Laboratoire de Mathématiques Jean Leray5 , Gilles Carron has been awarded the Leonid Frank Prize (€10,000). Gilles Carron's field of research is analysis on varieties. With K. Akutagawa and R. Mazzeo, he has shown that T. Aubin's criterion for the existence of conformal metrics with constant scalar curvature is valid for stratified spaces. In collaboration with I. Mondello, D. Tewodrose, he studied the Gromov-Hausdorff limits of sequences of Riemannian varieties whose Ricci curvature is controlled in a Kato class; this work generalizes that initiated by J. Cheeger and T. Colding.