Blaschke Products and the Crouzeix Conjecture

Explore the intricacies of Blaschke products and their connection to the Crouzeix conjecture in this 48-minute lecture by Pamela Gorkin from Bucknell University. Delve into the historical context of the Crouzeix Conjecture, examine numerical evidence, and investigate the role of model spaces and operator theory. Discover the properties of numerical ranges and Blaschke products, and learn how Sarason's 1967 work contributes to the discussion. Investigate the Level Set Conjecture (LSC) and its relationship to Blaschke products and level sets. Gain insights into practical applications of these mathematical concepts and consider natural questions arising from this exploration of complex analysis and functional theory.

Intro
The Crouzelx Conjecture
Finding numerical ranges
The Crouzex Conjecture: In the beginning
Numerical evidence
More of the evidence
Back to Greenbaum and Choi
Model spaces, operator theory and...
Blaschke products!
We know a lot about the numerical range
We also know a lot about Blaschke products
What Sarason's 1967 work tells us
Level Set Conjecture (LSC)
Blaschke products and level sets
Compare...
Application: LSC 6
Another Application
Natural Question