学术报告：Lyapunov exponents as an algebraic geometry invariant

发布时间：2014-10-16 【字体：大中小】

中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Dr. Charles Fougeron （Institut de mathématiques de Jussieu)

题目：Lyapunov exponents as an algebraic geometry invariant

时间：08.22（星期五）, 16:00--17:00

地点：数学院南楼N902室

摘要：

In my talk I will first introduce some background about these exponents, and explain in a second time to which extend we hope these exponents to be a new powerful geometric invariant in algebraic geometry, based on recent work of Kappes and Möller who showed non-commensurability of Deligne-Mostow non -arithmetic lattices ; and on some conjectures Kontsevich exposed recently at IHP in Paris.

The Lyapunov exponents have turned out to be a fundamental tool to understand SL(2, R) action on Teichmüller spaces. Anton Zorich and Maxim Kontsevich introduced these exponents in the 90's for any SL(2, R)-invariant submanifold in the Teichmüller space. Latter a link with variation of Hodge structure was pointed out by a theorem of Kontsevich and Forni, which states that the sum of these exponents is also the integral over the invariant locus of the curvature of the Hodge bundle. Thus we have a direct link between dynamical invariants (Lyapunov exponents) and algebraic geometry invariants (degree and euler caracteristic). More recently, Fei Yu has conjectured an even deeper bound between Lyapunov exponents and algebraic structure of the Hodge bundle through the Harder-Narasimhan filtrations.

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