168幸运飞艇计划

Abstract

I will illustrate the relationship among interval exchange transformation, rational polygonal billiards, flat surfaces and Teichmueller geodesic flows in the moduli space of abelian differentials.
Then we introduce Weierstrass filtrations to study the Harder-Narasimhan filtration of Hodge bundles on Teichmueller curves.It can be used to improve many recently results about the Lyapunov spectrum of Teichmueller curves， which is firstly appeared in Kontsevich-Zorich's 1997 paper "Lyapunov exponents and Hodge theory". Our results suggest a new conjecture on the relationship between Lyapunov exponents and Harder-Narasimhan filtrations on Teichmueller geodesic flows