Tits alternative and its application
彭俊文博士國家理論科學研究中心 15:30 – 17:00 鴻經館 M107
Abstract：
This talk will provide an in-depth exploration of the Tits Alternative, a crucial dichotomous property in group theory. It will trace its origins from the Banach-Tarski paradox to its interpretation through group theory by Van Neumann. The presentation will also highlight the role of the Ping-Pong Lemma, a key theorem in set theory, and the concept of growth rate in the understanding of the Tits Alternative. Further, the speaker will introduce the concept of dynamical canonical height and use it to prove the main result. The talk will conclude with a demonstration of how rational functions can exhibit either polynomial or exponential growth, and an examination of the practical applications of the Tits Alternative in the search for nontrivial solutions in functional equations.
20240222演講_ 彭俊文博士 (國家理論科學研究中心)