Many modern, large-scale datasets are structured as graphs, matrices, tensors, and other combinatorial objects. A central challenge across mathematics, statistics, and theoretical computer science is to understand the limits of inference, when these limits can be achieved computationally, and where fundamental barriers arise.
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.