Extremal Blaschke Products (19frg254)

The Banff International Research Station will host the "Extremal Blaschke Products" workshop in Banff from June 23, 2019 to June 30, 2019.

Finite Blaschke products are rational functions (quotients of polynomials) whose zeros lie in the unit disk, and which have modulus one on the unit circle. In many ways, they play the same role with respect to the unit disk that polynomials play in the complex plane.

The numerical range of a matrix is a convex set of numbers that both contains the eigenvalues and encodes numerous other properties of the matrix. Recent work in matrix theory has brought to light interesting connections between numerical ranges and finite Blaschke products.

The Blaschke products that arise via such connections are extremal in a certain sense. We expect that the study of these extremal Blaschke products will provide insight into a wide range of questions in matrix theory and complex analysis, including a related well-known open problem called the Crouzeix conjecture.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).