While landmark achievements by Perelman, Agol, and others have recently resolved major questions in dimension 3, the field of low-dimensional topology remains vibrant. Significant challenges persist—such as the L-space conjectureand the smooth Poincaré conjecture in dimension 4—alongside emerging questions at the intersection of various mathematical disciplines.
September 13 to 17 - Introductory school at IHP, Paris, amphitheater Hermite
October 11 to 15 - Workshop 1 at IHP, Paris: Advances in Quantum Cryptography: Information-theoretic Foundations
Recent trends at the interface between information theory, probability, statistics and high-dimensional geometry raise new questions on the role and importance of entropy in the understanding of both asymptotic and finite range phenomena, in particular towards discrete structures and applications to areas such as quantum information, percolation and random matrices. Recent fruitful developments warrant imminent blossom of new ideas and results in this area in the near future.
The program centers on the development of a unified understanding of kinetic theory in systems with long‑range interactions, with a particular emphasis on the quantum regime. Long‑range interacting quantum systems—realized experimentally in cold atoms, trapped ions, and polar molecules—exhibit rich dynamical behavior such as metastability, collisionless dynamics, anomalous transport, critical scaling, and turbulence‑like phenomena.
This Thematic Month aims to cover topics related to singularity theory of algebraic or analytic spaces, algebraic study of differential equations, and their applications to questions of transcendence.
The interface of mathematics with computer science form a large, diverse and rich landscape. Of course, many classical mathematical tools and concepts turn out to be very useful to answer questions arising from computer science. Besides, the core objects of computer science (typically discrete) that were once considered non-classical in mathematics have now a well-established and growing theory. In addition, the main ideas of computer science (the very notions of computation and algorithmic complexity) yield new points of views and new questions on many mathematical objects.
Scientific Machine Learning (SciML) is a relatively new research field based on both machine learning (ML) and scientific computing tools. Its aim is the development of new methods to solve several kinds of problems, which can be forward multidimensional partial differential equations, identification of parameters, or inverse problems. The methods we seek must be robust, reliable and interpretable. The new SciML tools allow the natural inclusion of data in the numerical simulation in order to generate new results.
The thematic month “Arithmetic and Information Theory” focuses on arithmetic geometry, information theory and their interplay.
The CEMRACS is a scientific event of the SMAI (the French Society of Applied and Industrial Mathematics). The concept was initiated in 1996 by Yvon Maday and Fr´ed´eric Coquel and takes place every year at CIRM in Luminy (Marseille, France) during 6 weeks from mid-July. The goal of this event is to bring together scientists from both the academic and industrial communities to work and discuss on focused topics. During the first week, a classical school is proposed. It consists of several lectures given by leading scientists and related to the topics of the research projects.