Non-dense Orbits in Moduli Space
Student No.:100
Time:Tuesday 10:30-11:30, 2018.1.2
Instructor:Yitwah Cheung [San Francisco State University]  
Place:Lecture Hall, 3rd Floor, Jin Chun Yuan West Bldg.
Starting Date:2018-1-2
Ending Date:2018-1-2

Date: Tuesday, 2 January 2018
Time: 10:30 am-11:30 am
Venue: Lecture Hall, 3rd Floor, Jin Chun Yuan West Bldg.

Speaker: Prof. Yitwah Cheung [San Francisco State University]

Title: Non-dense Orbits in Moduli Space
Abstract: While cataloguing and classifying the behavior of dynamical systems remains a daunting task, two important regimes have begun to emerge in the modern times.  In the parabolic regime, one expects to be able to understand the behavior of every single orbit, such as in the theory of unipotent flows and the more recent classification of orbits for the Teichmuller disk action.  In the hyperbolic regime, one can usually understand the behavior of most orbits--e.g. they will be dense inside some nice invariant locus, but there is also an abundance of orbits that behave in irregular ways, such being non-dense.  In this talk, I will describe some efforts to understand two kinds of non-dense orbits, namely bounded and divergent orbits, and the motivation coming from number theory.  If time permits, I will also explain how the study of the evolution of a geometric structure, as opposed to that of a featureless point, can be exploited to understand the dynamics on the moduli space.