On a New Subclass of Univalent Functions

Explore a lecture on a new analytic criterion for univalence of typically-real functions and the geometric properties of functions satisfying this criterion. Delve into the newly defined subclass Sc of univalent functions, which includes important functions like the Koebe function. Discover how extremal polynomials of orders 2, 3, and 4 belong to this family, and examine computer simulations suggesting that all such extremal polynomials are part of Sc. Gain insights into the Koebe quarter theorem and its connection to the presented subclass. Reference key works in the field, including Bieberbach's foundational paper, recent research on univalent polynomials, and the lecturer's own contributions to the subject.