Mathematics Colloquium: The Corona Problem

Speaker: Brett Wick, Washington University in St. Louis

Title:  The Corona Problem

Abstract:   The Corona problem has served as a major motivation for many results in complex function theory, operator theory, and harmonic analysis. In its simplest form, the question asks whether, given $N$ bounded analytic functions $f_1,\ldots,f_N$ on the unit disc such that $\inf (\left\vert f_1\right\vert+\cdots+\left\vert f_N\right\vert)\geq\delta>0$, it is possible to find $N$ bounded analytic functions $g_1,\ldots,g_N$ such that $f_1g_1+\cdots+f_Ng_N =1$. While the Corona problem is well-understood in the context of one complex variable, it remains highly challenging in the case of several complex variables.

In this talk, we will discuss some generalizations of the Corona problem to matrix-valued functions and their connections to geometry, to function spaces on the unit ball in several complex variables, and to setting a related question in the quaternions. The resolution of these questions relies on tools and methods from complex analysis, harmonic analysis, operator theory, and partial differential equations.

Date/Time: Friday, September 18, 3:30pm

Location: Exploratory Hall, Room 4106 or Zoom