Conférences  >  Mathématiques  >  Calcul infinitésimal, équations différentielles et intégrales

CIRM – Centre International de Rencontres Mathématiques

Solving time-harmonic wave equations with iterative methods is very challenging because they combine multiple difficulties like e.g. highly oscillatory solutions and complex non-Hermitian and indefinite discrete operators. In addition, the wave number associated to the numerical solution is different from the one of the exact solution thus leading to so-called numerical dispersion which requires very fine mesh to be controlled. There exists numerical schemes designed to reduce the dispersion error where the most used technique to build them relies on stencils involving free parameters that are next obtained by numerically minimizing the dispersion error. In the past few years, we develop an alternative approach called asymptotic dispersion correction. The latter is based on the introduction of a perturbation of the wavenumber (the shift) in the numerical scheme. We then explicitly compute the shift that minimizes the dispersion error for small enough meshsize. In addition, we show that our method can be applied to any finite difference scheme and reduces the relative error. We emphasize that most of works dealing with dispersion reducing methods consider the Helmholtz equation. The goal of the Research in Residence is to extend the asymptotic dispersion correction to the convected Helmholtz equation that can be used to model time-harmonic wave propagation in a moving flow.

Cours et évènements pour étudiants en mathématiques,    Analyse

The SCGAS is an annual conference on geometric analysis and related fields hosted jointly by UC Irvine and UC San Diego.

The 2025 SCGAS conference will feature the following speakers:

Simon Brendle (Columbia University)

Alice Chang (Princeton University)

Pengfei Guan (McGill University)

Lan-Hsuan Huang (University of Connecticut)

Christos Mantoulidis (Rice University)

Valentino Tosatti (New York University)

Ryan Unger (Stanford University)

Differential Geometry, Geometric Analysis

Géométrie et topologie,    Analyse

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Partial differential equations are a fundamental tool for modeling various physical phenomena and engineering problems. For example, oil flows in rock grains, turbulent filtration processes, groundwater flows, shallow water waves, phase changes of materials, and traffic congestion problems. The relevant PDEs are non-linear, and present certain degenerate and/or singular nature. Important examples include but are not limited to the porous medium equation, the p-Laplace equation, the total variation flow, the Stefan problem, doubly non-linear parabolic equations, widely degenerate equations, as well as related non-local equations.

Topics of the workshop include: (1) ​Gradient regularity for the porous medium/fast diffusion equation, (2) Wiener's criterion for non-linear parabolic equations, (3) Boundary Harnack estimates, (4) Regularity theory for Stefan-type problems, (5) Regularity theory for widely degenerate equations.

Cours et évènements pour étudiants en mathématiques,    Analyse

Harmonic analysis on homogeneous spaces is a fundamental area of research that simultaneously generalizes classical harmonic analysis on groups and on Riemannian symmetric spaces. It naturally relates to many areas of mathematics, playing a central role in representation theory and the theory of automorphic forms.

Representation Theory and Noncommutative Geometry

Analyse,    Algèbre

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.

Physique mathématique,    Mathématiques appliquées (en général)

Vanderbilt University

The conference will focus on several aspects of constructive function theory, including orthogonal polynomials, potential theory, discrete and continuous energy problems, special functions, polynomial inequalities, as well as various problems relating to optimization and efficiency. The aim is to stimulate collaboration and the exchange of ideas. The conference will be held in conjunction with the 37th Annual Shanks Lecture, to be given by Professor Doron Lubinsky (Georgia Institute of Technology).

Analyse,    Cours et évènements pour étudiants en mathématiques

University of Helsinki

Conference Quasiweekend III - Twenty years on collects together experts, from all fields of mathematics, using quasiconformal methods, especially in complex dynamics, geometric function theory, geometric group theory, analysis on metric spaces. Previous conferences in this series, Quasiweekend and Quasiweekend II – Ten years after, took place in 2005 and 2015, respectively, in Helsinki. With Quasiweekend III we celebrate mathematical legacy of Juha Heinonen -- initiator of this conference series -- in the broad field of quasiconformal analysis.

Email.: quasiweekend@gmail.com

Qusiconformal maps, complex dynamics, geometric function theory, geometric group theory, analysis on metric spaces

Analyse,    Géométrie et topologie

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Analyse,    Mathématiques numériques

CIRM – Centre International de Rencontres Mathématiques

The abstract foundation of the book concerning functional analysis, special issues on Sobolev type function scales, and elliptic and parabolic regularity in case of non-smooth data, is already solid. However, the culminating last part of the book is still under discussion and editing. There, it is intended, using the theory established before, to give a condensed and unified treatment of wellposedness for several real-world problems, namely the thermistor problem, the Keller-Segel chemotaxis model, and the macroscopic semiconductor equations (Van Roosbroeck system) in case of Avalanche generation, all for the case of non-smooth spatial domains. These problems were open for decades and solved only recently by the authors and collaborators in journal articles.

Analyse,    Mathématiques appliquées (en général)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)