Conferences  >  Mathematics  >  Calculus, Differential Equations and Integration  >  United States

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to exploring the theory of some nonlinear partial differential equations that appear as fundamental models in statistical mechanics and mathematical physics. Early investigations by Bernoulli, Maxwell and Boltzmann (∼1860) established the foundation of kinetic theory, and resulted in formulating the general equation of continuity, now known as the Boltzmann equation. The mathematical analysis of Boltzmann-type equations has led to decades of significant works, from Carleman in the 1930’s and up to the end of the past century with works by Cercignani, Di Perna, Lions, and many more. Research activity in the field has intesified in recent years, with the last two decades yielding numerous new results in regularity estimates, long time asymptotics, and global well-posedness. A particularly relevant line of research in this field is the study of diffusive integro-differential equations, which in addition to their role in statistical physics, has applications ranging from fluid mechanics to stochastic control and image processing. This workshops will bring together mathematicians working at the forefront of these two lines of research with junior researchers to focus on advancing specific open problems.

Two phase free boundary problems for diffusive integro-differential equations. Hypo-elliptic Hamilton-Jacobi-Bellman equations. Regularity theory for kinetic equations of Boltzmann and Landau type. Blow-down mechanism for Lenard-Balescu and other collision operators in plasma. Free boundary problems in chemotaxis.

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).

Analysis,    Courses and Events for Math Students and Early Career Researchers

Baylor University

The conference is organized around topics in harmonic analysis, linear and nonlinear partial differential equations, geometric measure theory, and scattering theory.

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.

Applied Mathematics (in general),    Mathematical Physics

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.

Applied Mathematics (in general),    Mathematical Physics

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