Trends in Complex Dynamics

May 16 -19, 2011


Clay Mathematics Institute
One Bow Street
4th Floor
Cambridge, MA

In the middle to late 1990's, the field of complex dynamics expanded its horizons considerably. Now rational maps, entire transcendental maps, and meromorphic functions are major topics of research. The behavior of these maps is often very different from that of polynomial maps. Furthermore, people have been investigating higher dimensional holomorphic maps like the planar Henon map. These types of maps were investigated at length back in the 1970's, but the lack of complex analytic tools hindered these efforts. Now this area is once again back in focus. And there are many other areas of interest: the structure of the set of rational maps near its boundary, algebraic dynamics, Newton's Method, etc.

The goal of this workshop was to convene a diverse group of experts in the various subareas of complex dynamics for an intense week of discussion of the different directions that complex dynamics is headed in.

Schedule

Monday, May 16

9:00-10:00	Kevin Pilgrim Polynomial dynamics on the basin of infinity
10:00-10:30	Break
10:30-11:30	Jeremy Kahn Geometric Limits and Renormalization
11:30-12:00	Break
12:00-1:00	John H. Hubbard Parabolic blowups: Kleinian groups and complex dynamics
1:00-2:30	Lunch
2:30-5:00	Breakout sessions, Harvard Math Dept, rooms 530 & 507
5:00-6:30	Reception, Hilbert Space, CMI
7:00	Dinner at the faculty club for invited guests

Tuesday, May 17

9:30-10:30	Nuria Fagella A separation Theorem for entire transcendental functions
10:30-11:00	Break
11:00-12:00	Xavier Jarque On the connectivity of the escaping set for complex exponential Misiurewicz parameters
12:00-1:30	Lunch
1:30-2:30	Monica Moreno Rocha Nonlanding hairs in transcendental entire dynamics
2:30-5:00	Breakout sessions, Harvard Math Dept, rooms 530 & 507

Wednesday, May 18

9:30-10:30	Serge Cantat Rational surfaces with a large automorphism group
10:30-11:00	Break
11:00-12:00	Volodia Nekrashevych Combinatorial models of expanding maps and Julia sets
12:00-1:30	Lunch
1:30-2:30	Adam Epstein Towards Arithmetic Thurston Rigidity
2:30-3:00	Break
3:00-4:00	Laura DeMarco Complex dynamics and arithmetic equidistribution

Thursday, May 19

9:00-10:00	Tan Lei Kneading sequences and irreducibility of quadratic periodic curves
10:00-10:30	Break
10:30-11:30	Daniel Meyer Expanding Thurston maps
11:30-12:00	Break
12:00-1:00	Mitsuhiro Shishikura Yoccoz tau-function and applications
1:00	Picnic/lamb roast, Harvard campus