Liding Yao - The Cauchy-Riemann problem via extension operators

The Cauchy-Riemann problem, also known as the $\overline\partial$-problem, is a central problem in several complex variables. It concerns the regularity estimates to the equation $\overline\partial u=f$ on forms in a bounded domain $\Omega\subset\mathbb C^n$. We will talk about the background of the $\overline\partial$-regularity theory, its obstructions, and our recent works using new technique from extension operator. We use the called the Rychkov's extension operator, which extends functions on a bounded Lipschitz domain and has boundedness on all Besov spaces and Triebel-Lizorkin spaces. This is partly joint with Ziming Shi.