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

Title: Dyadic analysis (virtually) meets number theory Abstract: In this talk we discuss two ways in which dyadic analysis and number theory share a rich interaction. The first involves a complete classification of "distinct dyadic systems". These are sets of grids which allow one to compare any Euclidean ball nicely with any dyadic cube, and

Title: Dyadic analysis (virtually) meets number theory Abstract: In this talk we discuss two ways in which dyadic analysis and number theory share a rich interaction. The first involves a complete classification of "distinct dyadic systems". These are sets of grids which allow one to compare any Euclidean ball nicely with any dyadic cube, and

Title: Necessary Conditions for Two Weight Weak Type Norm Inequalities for Multilinear Singular Integral Operators Abstract: In this talk we will discuss necessary conditions for a multilinear singular operator T to satisfy two weight weak type norm inequalities provided the kernel of T satisfies a weak non degeneracy condition. As an application of our techniques

Title: Poincare Inequalities and Neumann Problems for the p(.) Laplacian Abstract: In this talk, we discuss an established result proving an equivalence between weighted Poincare inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate p-Laplacian. We then extend this result to the variable exponent setting. We also

Title: Two weight bump conditions for commutators. Abstract: In this talk, we give some two weight conditions that are sufficient for the boundedness of commutators of Calderón-Zygmund operators.