This Bachelor seminar will cover introductory material in ergodic theory and topological dynamics and will focus on the study of measure-preserving transformations of probability spaces and continuous transformations of compact Hausdorff spaces.

The outline of topics is as follows:

• definitions and basic constructions (products, factors, induced transformations)
• examples (Bernoulli actions, odometers, circle rotations)
• ergodicity, freeness, recurrence, weak mixing, mixing, compact transformations
• the Rokhlin lemma
• mean and pointwise ergodic theorems
• entropy for probability-measure-preserving and continuous transformations
• possible advanced topics: multiple recurrence, Ornstein theory

There will be an organizational meeting on February 19, 2026, at 14:00 in room 503. If you are unable to attend in person, you may participate via Zoom. Please contact the organizer, David Kerr, for the Zoom coordinates.

• Topics in Ergodic Theory, by William Parry. Cambridge Tracts in Mathematics, 75. Cambridge University Press, Cambridge, 2004.
• Ergodic Theory, by Karl Petersen. Cambridge University Press, Cambridge, 1989.
• An Introduction to Ergodic Theory, by Peter Walters. Springer, New York, 2000.