Ilia Binder, University of Toronto

Title: Computability and Complexity in Complex Analysis and Complex Dynamics.

Abstract: In this talk, I will discuss recent advances in the computability of various objects arising in Complex Dynamics and Theory of Univalent functions. After a brief introduction to the general Computability and Complexity Theory, I will talk about the computational properties of polynomial Julia sets and conformal maps. I will also consider the computability questions related to the boundary extensions of conformal maps. Based on joint work with M. Braverman (Princeton), C. Rojas (Universidad Andres Bello), and M. Yampolsky (University of Toronto).RésuméIn this talk, I will discuss recent advances in the computability of various objects arising in Complex Dynamics and Theory of Univalent functions. After a brief introduction to the general Computability and Complexity Theory, I will talk about the computational properties of polynomial Julia sets and conformal maps. I will also consider the computability questions related to the boundary extensions of conformal maps. Based on joint work with M. Braverman (Princeton), C. Rojas (Universidad Andres Bello), and M. Yampolsky (University of Toronto).RésuméIn this talk, I will discuss recent advances in the computability of various objects arising in Complex Dynamics and Theory of Univalent functions. After a brief introduction to the general Computability and Complexity Theory, I will talk about the computational properties of polynomial Julia sets and conformal maps. I will also consider the computability questions related to the boundary extensions of conformal maps. Based on joint work with M. Braverman (Princeton), C. Rojas (Universidad Andres Bello), and M. Yampolsky (University of Toronto).