Sabbatical Plan: Complex Dynamics and Arithmetic Geometry

I plan to divide my sabbatical year between University of Michigan (Fall semester) and Stony Brook University (Spring semester). I am also planning a visit to Harvard University. The main scientific goal is to make progress towards a series of conjectures in complex and arithmetic dynamics, especially the "dynamical Andre-Oort conjecture" that was recently formulated by Matt Baker and myself. I work closely with faculty members at each of these institutions. I will visit Mattias Jonsson, Sarah Koch, and Michael Zieve at Michigan. I will visit Misha Lyubich, Jack Milnor, Eric Bedford, and Mattieu Arfeux at Stony Brook. I will visit Curt McMullen at Harvard.