题目： Unconventional ergodic averages
摘要：In this talk, we will report some recent progress on ergodic opitimization under certain constrained conditions. Precisely, we will investigate the maximal integral on physical-like measures, and the ergodic averages on the (ir)regular sets.
题目：Spatial entropy of symbolic dynamical systems
摘要：Spatial entropy is known to measure the complexity of symbolic dynamical systems. This talk concerns on two kinds of symbolic dynamical systems: shift spaces and multiplicative integer systems. They are essentially different. Shift spaces are shift-invariant, but multiplicative integer systems are multiplicative invariant. I will present our recent results about spatial entropy of them.
题目：Sobolev spaces and Besov spaces on the Sierpinski gasket
摘要：Function spaces have been a heated topic in analysis on fractals. Among them, Sobolev spaces which is defined with the Laplacian, and Besov spaces which depends only on the metric and measure, are of great interest. The fundamental but important question concerning the relationship between Sobolev spaces and Besov spaces was asked by R.S. Strichartz for fractal settings many years ago. Our work is the first one positively answering this basic question, which gives a perfect analog to the classical theorem. I will take the Sierpinski gasket as an example to illustrate our ideas. Atomic decomposition of Sobolev spaces will also be talked.