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