Dynamics, Algebra, and Number Theory
Douglas Lind
Abstract.
These lectures will treat the interactions between
algebraically defined dynamical systems and corresponding algebraic
objects. This leads to a rich "dictionary", new problems, and
fascinating connections. The main themes will include how algebraic
varieties, both complex and p-adic, and their amoebas help to
describe and analyse the dynamical properties of these algebraic
systems.
Tentative List of Topics:
- Perron numbers and entropy
- Expansive subdynamics of algebraic
-actions
- Amoebas: complex, p-adic, and adelic; connections with tropical
varieties
- Algorithmic problems in algebraic dynamics
- Actions of the discrete Heisenberg group and non-commutative Mahler
measure