Homogeneous Dynamics and Number Theory

Time and Venue:4, 5 FRI & 102

Course Objective:A lecture course devoted to understanding the interpaly of number theory and ergodic theory, topological dunamics in an important paper by Peter Sarnak.

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1, Wang Ke,Topological Entropy

2, Lou Miao, Invariant Measures and Measure Entropy

3, Wang Dan, Ergodic Theorems

4, Ji, The Geodesic and Horocycle Flows

5, Feng, Zhenzhen, Siegel Sets, Lattices and Mahler's Criterion

6, Ji, Sarnak's Conjectures

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Main References:

1, B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces. Cambridge University Press, Cambridge, 2000.

2, M. Einsiedler and T. Ward, Ergodic Theory with a view towards Number Theory, GTM 259.

3, M. Pollicott and M. Yuri, Dynamical systems and ergodic theory, CPU.

4, P. Sarnak, Three lectures on the Möbius function, randomness and dynamics.