for this workshop
Dynamics of multiple maps
at the
American Institute of Mathematics, Pasadena, California
organized by
Xander Faber, Patrick Ingram, and Bella Tobin
This workshop, sponsored by AIM and the NSF, 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.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than June 3, 2025. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
