This is an introductory course in ergodic theory, providing a comprehensive overlook over the main aspects and applications of this field.
In the broadest sense, ergodic theory is the study of group actions on
measure spaces. Its history traces from Poincare's recurrence theorem in
celestial mechanics and Boltzman's ergodic hypothesis in statistical
physics to its mathematical proliferation in the 1930s through the
ergodic theorems of von Neumann, Birkhoff, and Koopman. It has since
grown into a hugely important research area with striking applications
to other areas of mathematics, especially number theory and
combinatorics. This course provides an introduction to the basics of
ergodic theory. Among other things, this includes the theory of
recurrence, the structure and convergence of ergodic averages, and the
notion of entropy. We will motivate the main ideas and results through
simple examples. Another focal point lies on the many groundbreaking
applications of ergodic theory in number theory.
- Professor: Florian Karl Richter
- Teacher: Dimitrios Charamaras
