Simon Bortz is going to talk about the ideas in a recent paper which can be found at https://arxiv.org/abs/2008.11544. Roughly speaking, the talk will be about how a quantitative approximation scheme, in fact, gives a form of quantitative coincidence. The main theorem has some nice applications (e.g. transference of boundedness of singular integrals and `geometric

Title: Solvability of the Dirichlet Problem with L^p Data for Caloric Measure Abstract: This talk concerns two probability measures. First, we consider harmonic measure, which gives solutions to the Dirichlet problem associated to Laplace's equation. Additionally, we may view harmonic measure as the “hitting probability" for Brownian motion. This probabilistic interpretation shows the connection between

Title: Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces Abstract: In the Calderón-Zygmund Theory of Singular Integrals, the T(1) theorem of David and Journé is one of the most celebrated theorems. It gives easily-checked criteria for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^n), meaning T(f) is bounded for

Title: Novel Bellman Estimates for Ap Weights Abstract: The Bellman function method is an assortment of tools for obtaining sharp inequalities in harmonic analysis. To handle an inequality, one fixes a set of parameters, called Bellman variables, and maximizes (or minimizes) the left-hand side subject to these constraints. The solution of the corresponding extremal problem

Title: Some recent results on L_p-theory for equations with singular and degenerate coefficients Abstract: We consider classes of elliptic and parabolic equations whose coefficients are singular or degenerate of the porotype $x_d^\alpha$ on the domain $\{x_d >0\}, where $\alpha$ is a real number. Two boundary conditions on \{x_d =0\}$ are studied: the homogeneous Diritchlet boundary

Title: Anderson localization for disordered graphs Abstract: In this talk, we will discuss a mathematical treatment of a disordered system modeling localization of quantum waves in random media. We will show that the transport properties of several natural Hamiltonians on metric and discrete trees with random branching numbers are suppressed by disorder. This phenomenon is

Title: Suitable weak solutions of the Ericksen--Leslie system for nematic liquid crystal flows Abstract: In this talk, we will discuss the Ericksen--Leslie system modeling the hydrodynamics of nematic liquid crystals. It is a strongly coupled PDE system between incompressible Navier--Stokes equations for the underlying fluid velocity field and gradient-flow-like equations for the director field describing