Math 582CB
Symbolic and Algebraic Zd-Actions

Klaus Schmidt

Winter 2003, Monday/Wednesday/Friday 10:30-11:20

Contents:
  1. Multi-dimensional shifts of finite type: definition, undecidability problems, examples from statistical mechanics and other areas. Wang systems.
  2. Group shifts: multi-dimensional shifts of finite type with group structure. Mixing properties of group shifts and their connection with additive relations in fields with positive characteristic.
  3. Isomorphism rigidity of multi-dimensional group shifts.
Prerequisites: A basic understanding of measure theory (including Haar measure), elementary harmonic analysis (Pontryagin duality) and commutative algebra. The necessary results from these areas will be reviewed in the course.