Cornell Math - MATH 711, Fall 2003

MATH 711
Analysis and Stochastic Processes on Fractals
(Fall 2003)

Instructor: Takashi Kumagai

Meeting Time & Room

My plan is to choose topics on analysis and stochastic processes on fractals. The topics I have now in mind is the following:

1. Function spaces and stochastic processes on fractals (We determine function spaces corresponding to regular Dirichlet forms on fractals. We then study trace and embedding of the spaces, also study various properties of the corresponding stochastic processes.)
    
2. Stability of parabolic Harnack inequality and heat kernel estimates (We introduce various equivalence conditions for the parabolic Harnack inequality on fractals and discuss its stability.)
    
3. Homogenization on fractals (As an application of 2), we discuss homogenization problem on fractals.)

Since students may not be familiar with fractals, I will start my course from the introduction. I hope this plan fits the aim of the topic course.