Conférences  >  Mathématiques  >  Calcul infinitésimal, équations différentielles et intégrales  >  États-Unis

Institute for Computational and Experimental Research in Mathematics, Brown University, Providence, RI (ICERM)

A universal source of difficulty in the numerical solution of differential equations is stiffness, which may stem from multi-scale dynamics and means that straightforward explicit discretizations are very inefficient. Consequently, choosing how to deal with stiffness (usually through the selection of the time discretization method) is often the most impactful decision made while solving these problems; it can be the difference between complete intractability and rapid solution.

Simons Laufer Mathematical Sciences Institute (SLMath)

The Connections workshop will bring together leading experts working at the intersection of kinetic theory and stochastic partial differential equations (SPDEs). Kinetic theory is a body of theory for non-equilibrium statistical mechanics. The phase-space formulation provides the flexibility of characterizing dynamics emerging from a wide range of applications, ranging from rarified gas, to plasma, to photons, to bacteria. Complementing this, SPDEs provide powerful tools for modeling systems influenced by random fluctuations and noise, essential for capturing the inherent uncertainties in complex processes. This workshop will delve into how these cutting-edge mathematical techniques can be integrated to analyze and predict the behavior of systems ranging from fluid dynamics to financial models.

Mathématiques appliquées (en général),    Physique mathématique

Simons Laufer Mathematical Sciences Institute (SLMath)

The goal of the workshop is to introduce non-experts to two active research areas: kinetic theory and stochastic partial differential equations. Kinetic theory studies the properties of interacting particle systems modeling various processes in non-equilibrium statistical mechanics. Stochastic partial differential equations describe dynamics subjected to random noises. The methods from the two areas complement each other in studies of the phenomena arising in physics, economics, life sciences, etc.

Mathématiques appliquées (en général),    Physique mathématique

Society for Industrial and Applied Mathematics (SIAM)

Simons Laufer Mathematical Sciences Institute (SLMath)

The workshop aims to bring together researchers working on different facets of stochastic PDEs. The field of stochastic PDEs has seen many new techniques recently appear to tackle different problems, including renormalization, large scale and long-time behaviours, stochastic fluid dynamics, and homogenization. The goal of the workshop is to facilitate discussions and allow different communities to engage with one another one.

stochastic partial differential equations, regularity structures, paracontrolled calculus, nonlinear dispersive equations, Gibbs measures, homogenization, stochastic fluid dynamics, quantum field theory

ICERM/Brown University

The mathematical description of many-particle systems is a fundamental and challenging problem. At the microscopic level, particle interactions can be modeled with very large systems of ordinary differential equations. This approach can be impractical due to the very large dimension of the systems. Mean field models based on partial differential equations thus arise to describe the collective behavior of a large number of particles. Depending on the spatial and temporal scales, as well as the heterogeneity among particles, PDEs of different types and dimensions emerge. At the mesoscopic level, effective models are kinetic equations - including the Vlasov, Boltzmann, Landau equations - while at the macroscopic level we have continuum equations (for example, the Euler and Navier-Stokes equations). Beyond common mathematical challenges, microscopic, kinetic and fluid equations share a deeper link: Fluid equations can be obtained as a limit in certain asymptotic regimes from kinetic equations which, in turn, can be obtained by limits from microscopic models. This workshop aims at bringing together researchers working in these three connected areas from an analytical and computational perspective. These areas have seen dramatic progress over the last decade, and the methods and problems in each field are becoming highly relevant to the other fields. The meeting will showcase the most recent breakthrough results and promote interactions among communities and cross-pollination of techniques and mathematical methods.

Tél.: [4018635030];     Email.: info@icerm.brown.edu