Title: A Multi-scale Approach toĀ Limit Cycles with Random Perturbations Involving Fast Switching and Small Diffusion Abstract: This talk is devoted to multi-scale stochastic systems. The motivation is to treat limit cycles under random perturbations involving fastĀ random switching and small diffusion, which are represented by the use of two small parameters. Associated with the
Title: Cotlarās Inequality Abstract: We will go over Cotlarās classic inequality concerning the maximal truncation operator of a Calderon-Zygmund operator.Ā We will also cover some recent results for operators that satisfy a stronger Cotlar inequality.
Title: Optimal Transport on Finite Graphs with Applications Abstract: In this talk, I will discuss the optimal transport theory on discrete spaces. Various recent developments related to free energy, Fokker-Planck equations, as well as Wasserstein distance on graphs will be presented, some of them are rather surprising. Applications in game theory and robotics will be
Abstract:Ā In this talk I will give an over-view of the Stieltjes integral andĀ review some of the many definitions that appear in the literature.Ā I will talk about the strengths and weaknesses of each, particularly in relationship to the classical Darboux and Riemann integrals.Ā I will conclude with a discussion of a new definition
Title:Ā On the discrete Hilbert transform Abstract: Ā The discrete Hilbert transform, acting on the space of (doubly infinite) sequences, was introduced by David Hilbert at the beginning of the 20th century. It is the discrete analogue of the continuous Hilbert transform acting on functions on the real line (conjugate function in the periodic case).
Title: An overview of numerical algorithms for the Poisson-Boltzmann equation in biomolecular electrostatics Abstract: The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. The numerical solution of the PBE is known to be challenging, due to the consideration of discontinuous coefficients, complex geometry of protein structures,
Title:Ā Calderon-Zygmund theory for nonlinear partial differential equations and applications Abstract:Ā In this talk, we will discuss several recent developments on regularity theory estimates in Sobolev spaces for solutions ofĀ several classes of elliptic and parabolic nonlinear PDEs. Some classes of consideredĀ equations may be singular andĀ degenerate.Ā Important ideas and techniques will be highlighted. Connections and applications of the results