R201, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 201室)
2017 NCTS Short Course and Seminar on Dynamical Systems
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I. Speaker: Professor Jung-Chao Ban (National Dong Hwa University)
Time: 10:00-12:00 (Friday) from 9/22, 2017
Title: Short course on symbolic dynamics and ergodic theory
Abstract:
This short course focuses on three topics. Namely, the SFTs on Cayley graphs, open systems and arithmetic dynamics. For the first part we introduce the notions of the subshifts defined on the Cayley graphs and its entropies. The variation method which is used to compute the entropy are introduced herein. Such method leads us to characterize the entropies of the SFTs on Cayley graphs. For the second and third parts we introduce the open system and arithmetic dynamics, the former relates to physics and the latter relates to the number theory. We give the up-to-date survey of those two topics and to show how it relies on the theory of symbolic dynamics. The sub-topics of open systems contain the escape rate, conditional invariant measures and the entropy formula; the sub-topics of arithmetic dynamics contain the metric Diophantine approximation and shrinking target problems.
II. Speaker: Mr. Guan-Yu Lai (National Chiao Tung University)
Time: 13:00-15:00 (Friday) from 9/22, 2017
Title: Sarnak conjecture
Abstract:
This seminar is intended to provide studies and survey on Sarnak conjecture which include the various cases fulfill the conjecture, e.g., MMA-MMLS, discrete spectrum, distal flows, domain exchange, automatic sequences. The relation of the Chowla and the Sarnak conjecture will also be discussed herein.
