# The $\bar\partial$-problem on unbounded domains

In this talk, I will discuss recent progress with Phil Harrington on understanding the $\bar\partial$-problem in $L2$ and $L2$-Sobolev spaces on not necessarily pseudo-convex unbounded domains. I will discuss the challenges in moving from bounded to unbounded domains, and in particular, finding good defining functions, derivatives, and Sobolev spaces in which to work. Time permitting, I will conclude with a short explanation of how infinity can be thought of as a part of the boundary of the domain at which the metric and domain are poorly behaved.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.