Title: Computation of extension spaces in $kQ$-mod, for $kQ$ the path algebra of a quiver $Q$ of type $\tilde A(n-1,1)$, using planar curves. Abstract: The representation theory of quivers is important to the representation theory of associative algebras in general. If $Q$ is a quiver of affine type $\tilde A(n-1,1)$ and $k$ a fixed algebraically

Title:  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

Title:  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

Title:   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

Title: Deep neural network and numerical analysis - adversarial attack on image and videos Abstract: Deep neural networks have achieved state-of-the-art performance in a variety of fields. The exponential growth of machine learning models and the extreme success of deep learning have seen application across a multitude of disciplines. Recent works observe that a class of

Title: 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.

Title: 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 $F^{s,p}_q$

Title: 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