Pure Math colloquium

Eric Sawyer, McMaster University

“Corona problems - still open on the ball a half century after Carleson’s corona theorem in the unit disk.”

In 1962 Lennart Carleson showed that the maximal ideal space of the algebra of bounded analytic functions on the unit disk - the simplest of the ”nontrivial” Banach algebras - equals the closure of the point evaluations in the disk, thus demonstrating the absence of a ”corona”. While much progress has been made on extending this theorem to other algebras in one and more complex dimensions, the most natural extension still remains open today. Does the algebra of bounded analytic functions on the unit ball in higher dimensions have a corona? We will review the history of this classical problem, the many different attacks made on it, and some more more recent advances. The talk will be mainly expository, and some of the recent advances are joint work with Brett Wick.

Refreshments will be served in MC 5479 at 3:30 p.m. Everyone is welcome to attend.