Moduli spaces for algebraic dynamical systems

September 27 to October 1, 2021

at the

American Institute of Mathematics, San Jose, California

organized by

Laura DeMarco, Clay Petsche, and Joseph Silverman

Original Announcement

This workshop will be devoted to the study of the geometry and arithmetic of moduli spaces associated to dynamical systems on algebraic varieties, with a particular emphasis on dynamical systems on projective space.

The main topics for the workshop are:

The moduli spaces $M(N,d)$ are dynamical analogues of classical moduli spaces for curves and abelian varieties. They were constructed for $N=1$ in the 1990s, for all $N$ in the 2000s, and with portrait level structure $P$ quite recently, but we have only fragmentary knowledge of their geometry and arithmetic. Among the geometric questions that we hope to address during the workshop are compactifications of $M(N,d),$ the structure of the automorphism locus and the (generalized) critically finite locus, and geometric properties of portrait moduli spaces $M(N,d,P)$ as $P$ increases in complexity. Arithmetic questions that we plan to study include the analysis of the loci in $M(N,d,P)$ associated to uniform boundedness, good reduction, and field of moduli versus field of definition problems.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.