Computability and complexity of Julia sets.
Time and place
1 PM on Thursday, November 13th, 2014; NAC 6/113
Michael Yampolsky (University of Toronto)
Abstract
Informally speaking, a compact set in the plane is computable if one can write a computer program to visualize it with an arbitrarily high resolution. Julia sets are among the most drawn objects in mathematics, and numerical simulations provide much of the motivation for their study. Several years ago, M. Braverman and I showed that there exist quadratic polynomials with computable coefficients, whose Julia sets are not computable. I will explain the mathematics behind this somewhat counter-intuitive phenomenon, and will describe the current state of the subject. I will, in particular, discuss some open questions and conjectures on computational complexity of Julia sets, and the recent progress towards them.
