The Corona Problem on the Polydisk

Thur 17-July-2025 

Abstract

The Corona Problem is a fundamental question in complex analysis that originated from an inquiry about the boundary behavior of bounded holomorphic functions on the unit disk. While the problem was solved for the unit disk in the 1960s, extending the solution to higher dimensions, such as the polydisk, remains an important and challenging open problem.

This talk provides an introduction to the problem’s historical background and its formulation in several complex variables. We discuss the new geometric and analytic difficulties that arise in higher dimensions and highlight recent ideas and approaches aimed at advancing the understanding of the Corona Problem on the polydisk. The goal is to offer insight into a classical mathematical problem that continues to inspire research at the intersection of complex analysis and geometry.