After Newton’s discovery of the universal law of gravitation and Gauss’s discovery of the flux theorem for gravity, the main progress in the classical physics was the development of the Potential Theory, which provides the mathematical representation of gravitational fields. Modern Potential Theory is a field of Pure Mathematics in the cross-section of Analysis, Partial Differential Equations (PDE) and Probability Theory, and plays a crucial role for the study of many different phenomena in fluid dynamics, electrostatics and magnetism, quantum mechanics and probability theory. The conference will outline the major current developments in potential theory of elliptic and parabolic PDEs, nonlinear PDE systems in fluid mechanics, including the regularity of weak solutions, Wiener-type criteria for the boundary regularity, regularity of the point at infinity and its probabilistic, measure-theoretical and topological consequences, criteria for the removability of singularities of PDEs representing natural phenomena, singularities of the Navier-Stokes equations, free boundary problems, asymptotic laws for the diffusion processes, conditional Brownian processes, fine and minimal-fine topology and other related topics.
Conferences
