Representation theory and analysis on homogeneous spaces
Théorie des représentations et Analyse sur les espaces homogènes
21 September – 2nd October, 2026
Chair > Ali Baklouti
University of Sfax, Tunisia
Ali Baklouti is a Full Professor of Mathematics at the University of Sfax, Tunisia, and Director of the research laboratory LAMHA.
His research focuses on representation theory and geometric and harmonic analysis on homogeneous spaces. He served as Vice-President of the University of Sfax (2020–2024) and was President of the Tunisian Mathematical Society (2016–2023). As co-founder and Deputy Director of the Mediterranean Institute of Mathematical Sciences since 2012, he was also elected a permanent member of the Tunisian Academy of Sciences in 2016.
Co-Chair > Michael Pevzner
Université de Reims Champagne-Ardenne, France
Michael Pevzner is a Research Professor at the Laboratoire de Mathématiques de Reims where he works in the field of Lie group representation theory. Professor Pevzner is also the Director of the French-Japanese Laboratory of Mathematics and its Interactions (FJ-LMI) in Tokyo.
« Mathematicians often like to give rather imaginative and obscure names to the concepts they study. In reality, this field is about exploring the symmetries of objects — often infinite-dimensional — that frequently arise in the context of quantum physics. »
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INTRANET FOR ORGANIZERS
RESEARCH SCHOOL
Representation Theory, Geometry, and Quantization on Homogeneous Spaces
Théorie des représentations, géométrie et quantification sur les espaces homogènes
21 – 25 September, 2026
This research school, organized as a part of the « Chaire Pays du Sud 2026 » activities at CIRM, will bring together internationally renowned experts to deliver a series of advanced lectures on key topics in representation theory, the geometry of homogeneous spaces, harmonic analysis, and deformation quantization.
The school is intended for graduate students, postdoctoral researchers, and early-career academics, particularly those from the Global South, and will offer a comprehensive introduction to the deep interplay between algebra, geometry, and analysis. Each course is designed to be both accessible and substantial, with a strong emphasis on foundational concepts as well as recent developments.
Fanny Kassel will survey major results on proper actions of discrete subgroups on homogeneous spaces of reductive Lie groups, a topic that intersects differential geometry, Lie theory, and dynamical systems. The study of these actions not only informs geometric structures on manifolds but also underpins analytic tools for spectral theory.
Toshiyuki Kobayashi will present recent progress in the spectral analysis of locally symmetric spaces, focusing on non-Riemannian settings and exploring the interplay between representation theory and global analysis. His lectures will highlight how this theory connects with proper group actions, a theme expanded upon in Fanny Kassel’s course.
Dominique Manchon will explore the interface between deformation quantization and representation theory, focusing on nilpotent and solvable Lie groups. Topics include Poisson geometry, Kontsevich’s formality theorem, and the orbit method, which links the geometric theory of coadjoint orbits with the algebraic construction of representations.
Angela Pasquale will delve into the Howe correspondence over the reals, tracing the emergence of the Weil representation and its realization in various models. Her lectures will address the classification of reductive dual pairs and provide insight into the structure and applications of theta correspondences, touching on their implications in number theory and physics.
By covering a broad spectrum from geometric group actions to quantization techniques and dualities in representation theory, this school will equip participants with essential tools to engage in cutting-edge research. The interaction among the courses will offer a unified perspective on a vibrant and active area of mathematics, while also identifying open problems and future directions.
COURSES
Fanny Kassel (CNRS, IHES) Proper actions on reductive homogeneous spaces
Toshiyuki Kobayashi (University of Tokyo) Spectral analysis on locally symmetric spaces
Dominique Manchon (CNRS, Université Clermont-Auvergne) Deformation quantization and representations
Angela Pasquale (Université de Lorraine) The Howe correspondence over the reals
WORKSHOP
Representation Theory and Harmonic Analysis on Homogeneous Spaces
Théorie des représentations et analyse harmonique sur les espaces homogènes
28 September – 2nd October, 2026
This international workshop brings together leading experts and early-career researchers to explore the latest advances in representation theory, harmonic analysis, and their geometric and analytic aspects on homogeneous spaces. Building on the foundational themes introduced during the preceding research school, this workshop will focus on cutting-edge developments at the crossroads of Lie theory, geometric analysis, quantization, and differential geometry. Particular emphasis will be placed on the interaction between algebraic structures and analytic methods, including the role of coadjoint orbits, spectral theory, proper group actions, dualities, and deformation quantization.
The event will serve not only as a platform for disseminating recent research results but also as a fertile ground for collaborative discussions and new ideas. We are especially committed to supporting the participation of promising young mathematicians from the Global South, fostering a diverse and inclusive mathematical community. Through a combination of plenary talks, thematic sessions, and informal exchanges, this workshop aims to strengthen existing collaborations and stimulate future research directions in a field of central importance to modern mathematics and its applications in several branches of mathematics, such as physics and number theory, etc.
RESEARCH IN RESIDENCE 1
Analysis, Representations, and Geometry on Homogeneous Spaces
Analyse, représentations et géométrie sur les espaces homogènes
October 5-16, 2026
Participants
Ali Baklouti (Université de Sfax)
Junko Inoue (Tottori University)
Toshiyuki Kobayashi (University of Tokyo) to be confirmed
Michael Pevzner (Université de Reims)
The research-in-pairs gathering of Professors Toshiyuki Kobayashi, Michael Pevzner, Ali Baklouti, brings together leading experts in representation theory, global analysis, and geometric quantization. This collaborative session aims to explore cutting-edge interactions between harmonic analysis on homogeneous spaces, coadjoint orbit methods, and the geometric and analytic aspects of representation theory for real Lie groups. Special attention will be given to the analysis on pseudo-Riemannian locally symmetric spaces, the orbit method for solvable and nilpotent groups, and the extension of quantization procedures to singular settings. The combination of different yet deeply connected perspectives promises to generate new insights and advance current understanding in this highly active domain of mathematics.
RESEARCH IN RESIDENCE 2
Operator Algebras and Noncommutative Geometric Analysis
Algèbres d’opérateurs et analyse géométrique non commutative
October 19-30, 2026
Participants
Lobna Abdelmoula (Université de Sfax)
Ali Baklouti (Université de Sfax)
J. B. Kayoya (Université du Burundi)
Michael Pevzner (Université de Reims)
The research-in-pairs gathering of Michael Pevzner, Ali Baklouti, Lobna Abdelmoula, and Jean-Boscou Kayoya, focuses on the study of moment maps and their deep connections to representation theory and symplectic geometry. This collaboration aims to investigate the geometric and algebraic structures underlying moment sets associated with unitary representations, particularly in the context of nilpotent and solvable Lie groups. By combining techniques from deformation quantization, invariant theory, and the geometry of orbits, the group seeks to advance the understanding of the role of moment maps in the orbit method and their implications in the classification of representations. The participation of researchers from both the Global South and established international institutions enhances the diversity of approaches and contributes to the broader goals of mathematical collaboration and knowledge exchange promoted by the Chaire Pays de Sud.
SPONSORS
