摘要：One of central problems in ergodic theory is deciding when two measurable dynamical systems are measurably conjugate. The usual way to tackle the problem is to look for measure-isomorphism invariants. Entropy is one of the most important such invariants. In this talk, I shall give a survey of entropy theory for countable discrete group actions, including recalling the classical entropy theory for the integer group action and discussing recent progress about entropy theory for countable amenable group actions and then for countable sofic group actions.

My talk is based on a series of joint works with A. Dooley (UK), T. Downarowicz & D. Huczek (Poland), W. Huang & X. D. Ye (China) and N.-P. Chung (Vietnam).