Moduli spaces for algebraic dynamical systems
September 27 to October 1, 2021
American Institute of Mathematics,
San Jose, California
and Joseph Silverman
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.
- The geometry of $M(N,d),$ the moduli space of degree d endomorphisms
- Arithmetic problems associated to rational points on $M(N,d).$
- Dynamical moduli spaces associated to non-rational varieties, such
as $K3$ surfaces, that admit non-trivial endomorphisms.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.