Program
Entropy for actions of sofic groups
Student No.:50
Time:Tue/Thu 15:10-17:00, 2016-11-08~ 2016-12-01 (No classes on public holidays)
Instructor:Hanfeng Li  [SUNY at Buffalo]
Place:Conference room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-11-8
Ending Date:2016-12-1

 

 

Description:

 

 

Entropy is one of the most important invariants in dynamical systems, in both measure-theoretic and topological settings. The original Kolmogorov-Sinai entropy was introduced for integer group actions in late 1950s and extended to amenable group actions in 1970s. After the break-through of Lewis Bowen in 2010, there is now a well-founded theory of entropy for actions of sofic groups. In this course we shall discuss the following topics:

 

1.    Amenable groups.

 

2.    Entropy for actions of amenable groups.

 

3.    Calculation of entropy for Bernoulli actions of amenable groups.

 

4.    Sofic groups.

 

5.    Entropy for actions of sofic groups.

 

6.    Calculation of entropy for Bernoulli actions of sofic groups.

 

7.    Gottschalk’s surjunctivity conjecture.

 

 

 

Prerequisite:

 

 

Real analysis

 

 

 

Reference:

 

 

Chapters 3, 8 and 9 of The book “Independence and Dichotomies in Dynamics” by Kerr and Li:

http://www.math.tamu.edu/%7Ekerr/book/