Abstract: In this talk, I will discuss computability questions arising in Complex Dynamics and Complex Analysis. More specifically, I will discuss the existence of non-computable polynomial Julia sets and of polynomial Julia sets with arbitrarily high computational complexity. I will also discuss the conditions necessary and sufficient for the computability of conformal maps and their Caratheodory extensions. The computability of another central object of Complex Analysis, the Harmonic measure, will also be discussed. A crash course in general Computability Theory will be given. The talk is based on joint projects with M. Braverman (Princeton), A. Glucksam (Northwestern), C. Rojas (Universidad Catolica de Chile), and M. Yampolsky (University of Toronto). 

Bio-Sketch: Ilia Binder is a professor at the University of Toronto and the chair of the Department of Mathematical and Computational Sciences at the University of Toronto Mississauga. He obtained his bachelor's degree from St. Petersburg State University and his Ph.D. from the California Institute of Technology. He then held positions at IAS Princeton, Harvard, and UIUC before moving to the University of Toronto. He has a very broad interest in mathematics and produced more than 30 papers in areas including Geometric Function Theory, Statistical Physics, Probability, Computational Complexity, and Dynamical Systems. 

Tencent Meeting: 171 469 177