Analysis Seminar : Malik Younsi (University of Hawaii)

When:
September 5, 2017 @ 3:30 pm – 4:30 pm
2017-09-05T15:30:00-10:00
2017-09-05T16:30:00-10:00
Where:
Keller 402

This semester, the Analysis Seminar will meet on Tuesdays 3:30 – 4:20 pm in Keller 402.

Title :

What are the possible shapes of polynomial Julia sets?

Abstract :

Ever since the digital revolution and the emergence of computers, mathematicians have been fascinated by fractals, those geometric figures showing self-similar patterns and irregular structures. A well-known family of fractals introduced by Gaston Julia and Pierre Fatou in the early 20th century are the so-called Julia sets, obtained from the iteration of a polynomial of one complex variable. It has been known for a long time how rich and diverse the geometry of these Julia sets are, from Cantor sets to smooth curves as well as highly irregular figures.

But what exactly are the possible shapes of polynomial Julia sets? This question, raised by Bill Thurston shortly before he passed away, has a rather surprising answer : they can have any shape, except some trivial topological obstructions. In this talk, I will present the ideas underlying the proof of this result, which gives an explicit construction. In particular, we will see how potential theory comes into play. I will also discuss some related computational aspects.