Chih-Hung Chang
( National University of Kaohsiung)
The purpose of this seminar is to provide a forum for scholars exchanging their ideas and to seek for sparks inspired by different aspects of dynamical systems. In this seminar, we will mainly focus on the issue arising in the ergodic theory and collective dynamics. Ergodic theory is widely applied in variety of areas such as number theory, biology, and fractal geometry, ect. The survey and state-of-the-art of topological and measure-theoretic properties of dynamical systems over amenable and sofic groups is presented herein. Some open questions will be raised in the seminar and hope to solve them together. Collective dynamics describes the coherent inphase motion between a group of agents. These phenomena such as flocking of birds, schooling of fishes and swarming of bacteria are often observed in the biological systems. The Cucker-Smale model is one of the classical models in the literature to descript these. In this seminar, some important works related the model will be survey and some open questions will also be raised.