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CIRM – Centre International de Rencontres Mathématiques

This project focuses on the development of unconditionally stable conforming space—time methods for the linear time‑dependent Schrödinger equation. The main challenge is to overcome the lack of inf‑sup stability in the standard Petrov‑Galerkin formulation for this equation. In fact, the conforming space—time finite element discretization requires a restrictive CFL condition. To address this issue, we propose two approaches. ‑The first one is to augment the sesquilinear form of the standard scheme by adding a carefully chosen inconsistent penalty term to improve the discrete properties of the scheme. By introducing this term, we aim to improve stability without compromising convergence order. ‑The second approach involves the composition of the continuous sesquilinear form with an appropriate transform of the test functions. This modification aims to endow the new sesquilinear form with higher stability properties than its unmodified counterpart.

Applied Mathematics (in general),    Computational Physics and Numerical Simulation

CIRM – Centre International de Rencontres Mathématiques

The idea of making space noncommutative is probably as old as quantum mechanics, but it has developed considerably since the mid 80’s in various directions, from pure mathematics to theoretical physics, yielding some phenomenological predictions in high energy physics. The aim of this conference is the interplay between noncommutative geometry and physics.

CIRM – Centre International de Rencontres Mathématiques

The conference, in advance of a thematic program planned for IHP in 2026, addresses the key role played by completely integrable systems as models for wave phenomena in myriad physical settings such as surface water waves and internal waves, quantum excitations in Bose-Einstein condensates, plasma oscillations, optical fiber telecommunication systems, and solid-state physics. The principal objectives of the CIRM conference are to focus specifically on soliton gases, explicit formulas, and asymptotic behavior in integrable models, and to highlight corresponding novel results and new progress on several previously impenetrable fronts.

Calculus, Differential Equations and Integration,    Applied Mathematics (in general)