Dynamics of multiple maps
November 3 to November 7, 2025
at the
American Institute of Mathematics,
Pasadena, California
organized by
Xander Faber,
Patrick Ingram,
Michelle Manes,
and Bella Tobin
Original Announcement
This workshop will be devoted to studying arithmetic dynamics of multiple maps. In classical arithmetic dynamics, we consider the iteration of a single
endomorphism of a variety defined over a field of arithmetic interest — typically a number field or the function field of a curve.
An exciting new direction in arithmetic dynamics that holds particular promise for striking new results is what we call "dynamics of multiple maps": dynamical behavior arising from the interaction of two or more endomorphisms on the same space. This includes iteratively applying rational functions on $\mathbb{P}^1$ chosen at random from a family according to some probability distribution; a correspondence from a variety $X$ to itself; and forming words from a non-commuting family of involutions on a K3-surface.
Our goal for this workshop is to leverage analogies and direct connections between these seemingly disparate settings to ask new questions, make new conjectures, and explore how proof strategies in one context may port to another.
The main topics for this workshop are
- the arithmetic of orbits for semigroup and stochastic dynamical systems,
- the arithmetic of orbits for correspondences on a variety,
- common preperiodic points of complex rational functions, and
- finite orbits for non-commuting K3-surface automorphisms.
Material from the workshop
A list of participants.
The workshop schedule.
Workshop videos
