Here is a collection of my study notes, talk notes, and presentation slides.

Ergodic Theory

• Geometric form of Oseledets’ Multiplicative Ergodic theorem - A talk notes on Oseledets’ Multiplicative Ergodic Theorem (MET), trying to discribe a geometric framework of this theorem pioneered by Kaimanovich.
• Notes on ergodic proof of Roth theorem (in Chinese) - A reading notes on Furstenberg's corresponding principle and ergodic proof of Roth theorem on arithmetic progress of length 3.
• Notes on mixing limit theorems - A talk notes on general framework of how to upgrade a limit theorem to mixing limit theorem.

Translation surfaces and Teichm$\ddot{\mathrm{u}}$ller dynamics

• Notes on Siegel-Veech transform - A reading notes on Siegel-Veech transform and its connection to counting holonomy vectors on translation surfaces.