Research Seminar in

continues to meet in G5 (Rolla Building)

on Wednesday, Oct 11, 2000, 3:30 pm.

All interested faculty and students are invited to attend.

Kevin Pilgrim will talk on
Combinatorial Rigidity in Complex Dynamics.

A beautiful aspect of complex dynamics is the abundance of combinatorial rigidity phenomena, that is, instances where the geometry of a dynamical system is faithfully encoded by purely combinatorial information (e.g. a rational number, a homotopy class, a fundamental group, ...). In this talk I'll discuss three manifestations of this phenomena: in the quadratic family $z \mapsto z^2 + c$ (Yoccoz); in the family of postcritically finite rational maps (Thurston); and in the family of dynamical Belyi polynomials. I'll also discuss the implications of a very recent result on the failure of rigidity: the combinatorial rigidity conjecture fails for the family of cubic polynomials (C. Henriksen).