Explore polynomial approximation techniques for inverses of functions in Dirichlet-type spaces in this 49-minute lecture by Catherine Beneteau from the University of South Florida. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute, delve into topics such as optimal approximants, cyclicity, and convergence. Examine the importance of studying polynomials and their role in function approximation. Investigate the challenges faced in calculating optimal approximants, analyzing zeros, and determining cyclicity. Gain insights into the convergence properties of these approximations and participate in a Q&A session to further your understanding of this complex mathematical subject.