# Simon Bortz

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

ZoomTitle: Matrix weights, the convex-set valued maximal operator, and Rubio de Francia extrapolation part 2. 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

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

ZoomTitle: Matrix weights, the convex-set valued maximal operator, and Rubio de Francia extrapolation part 3. Abstract: In this series of talks, 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 my

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

ZoomTitle: Matrix weights, the convex-set valued maximal operator, and Rubio de Francia extrapolation part 4. Abstract: In this series of talks, 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 my

### Analysis Seminar – Walton Green (Washington University)

ZoomTitle: Wavelet Representation of Smooth Calderón-Zygmund Operators Abstract: We represent a bilinear Calderón-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a sparse T(1)-type bound, which in turn yields directly new sharp weighted linear and mutlilinear

### Analysis Seminar – Simon Bortz (University of Alabama)

ZoomTitle: A free boundary problem for the heat equation. Abstract: In his breakthrough result, it was shown by Dahlberg that the L^2 Dirichlet problem for the Laplacian (harmonic functions) is solvable in the region above a Lipschitz graph. Dahlberg did this by showing a local reverse Hölder inequality for the Poisson kernel in such domains.

### Analysis Seminar – Armin Schikorra (University of Pittsburgh)

ZoomTitle: A Harmonic Analysis perspective on $W^{s,p}$ as $s \to 1^-$. Abstract: We revisit the Bourgain-Brezis-Mironescu result that the Gagliardo-Norm of the fractional Sobolev space W^{s,p}, up to rescaling, converges to W^{1,p} as s\to 1. We do so from the perspective of Triebel-Lizorkin spaces, by finding sharp $s$-dependencies for several embeddings between $W^{s,p}$ and $F^{s,p}_q$

### Analysis Seminar – Ryan Alvarado (Amherst College)

346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Optimal embeddings and extensions for Triebel-Lizorkin and Besov spaces in spaces in quasi-metric measure spaces. Abstract: Embedding and extension theorems for certain classes of function spaces in $\mathbb{R}^n$ (such as Sobolev spaces) have played a fundamental role in the area of partial differential equations. In this talk, we will discuss some recent work which

### Analysis Seminar – Simon Bortz

Title: Heat extensions of doubling weights and A_infty A_infty weights play a fundamental role in weighted inequalities for operators used in harmonic analysis. It is known that if w is an A_infty weight then log w in the space of bounded mean oscillation (BMO) and the converse is `almost’ true (up to taking a

### Analysis Seminar – Brandon Sweeting

302 Gordon Palmer HallTitle: Mixed Weak-Type Estimates for Classical Operators Abstract: We prove new mixed weak type estimates for various classical operators of Harmonic analysis. Mixed weak type inequalities were first studied by Muckenhoupt and Wheeden and later by Sawyer to prove the $L^p$ boundedness of the Hardy-Littlewood maximal operator as a consequence of the Jones factorization

### Analysis Seminar – Atanas Stefanov

231 Gordon Palmer HallTitle: On the long term dynamics of the Landau-DeGennes gradient flow Abstract: We study the gradient flow of the Landau-deGennes energy functionals, in the physically relevant spatial dimensions $d=2,3$. We establish global well-posedness and global exponential time decay bounds for large $H^1$ data in the 2D case, and uniform bounds for large data in 3D.