This seminar, organized by Arthur Bartels
and David Kerr,
will cover the basic theory of entropy for probability-measure-preserving
(p.m.p.) actions of amenable and sofic groups and include recent results
on the invariance of entropy under Shannon orbit equivalence. No prior knowledge of ergodic theory will be assumed.
The seminar is suitable for Master's and Ph.D. students.
The main resource will be the book
Ergodic Theory: Independence and Dichotomies,
to which section numbers in the schedule below refer.
If you are interested in participating in the seminar please contact one of the organizers.
The seminar takes place Tuesdays 14:00-16:00 in SRZ 203, starting April 12.
Schedule
1 — April 12, Arthur Bartels
Measure theory background, p.m.p. actions,
basic examples including Bernoulli actions and odometers (§1.2–1.6, 2.3.1, 2.3.4)
2 — April 19, Flóra Benedek
Basic ergodic theory: ergodicity, freeness, weak mixing, compact actions (§2.1–2.2)
3 — April 26, David Kerr
Amenable groups, Følner property, mean ergodic theorem for p.m.p. actions of amenable groups
(§4.1, 4.3)
4 — May 10, James O'Quinn
Shannon entropy and Boltzmann entropy (§9.1–9.2, 10.1)
5 — May 17, Antje Dabeler
Measure entropy for p.m.p. actions of amenable groups (§4.7, 9.3)
6 — May 24, Julia Semikina
Pointwise ergodic theorem and Shannon–McMillan–Breiman theorem for p.m.p. ℤ-actions [3,4]
7 — May 31, Bastian Müller
Amenable entropy generator theorem, computation of entropy for Bernoulli and compact actions
(§9.4–9.6)
8 — June 14, Julian Kranz
Sofic groups, measure entropy for p.m.p. actions of sofic groups (§10.2–10.3)
9 — June 21, Giles Gardam
Sofic entropy generator theorem, computation of entropy for Bernoulli and compact actions
(§10.4–10.6)
10 — June 28, Diego Martínez
Invariance of entropy under Shannon orbit equivalence for p.m.p. ℤ-actions [2]
Resources