"The Bohr Radius Problem in Several Complex Variables"

Abstract : In 1913, H. Bohr proved a result concerning the convergence of the series of the moduli of a power series' coefficients in one dimension. Finding a solution to the same question in higher dimensions is usually called the Bohr radius problem. In this lecture, I will talk briefly about the history of the Bohr radius problem, and look at the developments so far. In 2014, it was proven by F. Bayart, D. Pallegrino, and J. B. Seoane-Sepulvida, that the exact asymptotic for the Bohr radius is the square root of log(n)/n, where n is the dimension. I shall conclude the lecture by discussing some of the questions in this topic that still need to be answered.

Host: John McCarthy