The combinatorial theory of one-complex dimensional holomorphic dynamical systems
has recently grown in several unexpected ways: new constructions in Teichmuëller theory
give deformation spaces recently shown by to be disconnected by S. Koch and E. Hironaka,
and by T. Firsova, J. Kahn, and N. Selinger. L. Bartholdi and D. Dudko give innovative
algebraic invariants similar to graph-of-groups constructions. D. Thurston introduced one-real-dimensional
invariants, somewhat analogous to train tracks, that give alternative characterizations
of rational maps. These are related to conformal invariants that find
applications in other settings. Recent software packages by L. Bartholdi (here) and
W. Parry et. al. (here) give us tools for
studying
concrete examples. Progress in the study
of subdivision rules by M. Bonk-D. Meyer and by W. Floyd-W. Parry-K. Pilgrim also give new combinatorial
invariants. Finally, it turns out one-complex dimensional
dynamical systems induce interesting higher-dimensional holomorphic dynamical systems.
This session will bring together researchers–including several recent PhDs–with diverse
backgrounds and a common interest in conformal dynamics and geometry. It will also be a
valuable networking opportunity for several graduate students in the region who have
passed their qualifying (oral) examinations and are beginning in-depth study of related
topics.