# Simon Bortz

### Analysis Seminar – Brandon Sweeting (University of Cincinnati)

ZoomTitle: 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

### Analysis Seminar – Tuoc Phan (University of Tennesse, Knoxville)

ZoomTitle: 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

### Analysis Seminar – Selim Sukhtaiev (Auburn University)

ZoomTitle: 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

### Analysis Seminar – Hengrong Du (Purdue University)

ZoomTitle: 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

### Analysis Seminar – Tess Anderson (Purdue University)

ZoomTitle: 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

### Analysis Seminar – Tess Anderson (Purdue University)

ZoomTitle: 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

### Analysis Seminar – John Oliver MacLellan (University of Alabama)

ZoomTitle: 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

### Analysis Seminar – Michael Penrod (University of Alabama)

ZoomTitle: 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

### Analysis Seminar – Quan Tran (University of Alabama)

ZoomTitle: 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.

### Analysis Seminar – David Cruz-Uribe, OFS (University of Alabama)

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Matrix weights, the convex-set valued maximal operator, and Rubio de Francia extrapolation Abstract: In this series of talks (I project three), I want to talk about the theory of matrix weights: its history and motivation, and some recent results by myself, Kabe Moen, and others. The ultimate goal is to give an overview of