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).