## 邵松: Recent progress on topological sequence entropy

First we will recall some basic results about topological sequence entropy. Then we focus on the maximal pattern entropy h^*(T), which is defined as \sup_S h_S(T), S ranging over all subsequence of non-negative numbers. By Huang-Ye, h^*(T)\in \{log k: k\in N\}\cup \{\infty \}. Recently, Snoha, Ye and Zhang showed that for any subset B of \{log k: k\in N\}\cup \{\infty \} containing 0, one can find a space X such that B=\{h^*(T): T is a continuous selfmap of X \}. Huang, Lian, Shao and Ye showed that if h^*(T) is bounded, then it has very nice structure. To be precise, we showed that for a minimal system (X,T), if h^*(T) is finite, then it is an almost finite to one extension of its maximal equicontinuous factor, and it has only finitely many ergodic measures.