|Some classification programs in dynamical systems|
|Time：||Mon/Wed 13:00-14:50, 2016-07-11 ~ 2016-07-20|
|Instructor：||Nhan Phu Chung [Sungkyunkwan University]|
|Place：||Conference Room 4, Floor 2, Jin Chun Yuan West Building|
In this course, we will introduce dynamical systems in both continuous and measurable settings. We will present classification programs of dynamics and their relations with geometric group theory and operator algebras. More precisely, we are planning to describe
1) The work of Lewis Bowen on the classification of Bernoulli shifts over sofic groups using entropy.
2) Cocycle superrigidity and orbit equivalence superrigidity.
Measure Theory and Real Analysis.
1) Lewis Bowen, Measure conjugacy invariants for actions of countable sofic groups, J. Amer. Math. Soc., 23 (2010), 217-245.
2) Valerio Capraro, and Martino Lupini, Introduction to Sofic and hyperlinear groups and Connes' embedding conjecture, with an Appendix by Vladimir Pestov, Lecture Notes in Mathematics, 2136. Springer, Cham, 2015.
3) Nhan-Phu Chung and Yongle Jiang, Continuous cocycle superrigidity for shifts and groups with one end, arXiv:1603.00114.
4) Xin Li, Continuous orbit equivalence, preprint, arXiv:1503.01704.
5) Sorin Popa, Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups, Invent. Math. 170 (2007), no. 2, 243–295.