The main goal of this course will be to analyze the structure of orbits of polynomial transformations of the affine space of dimension m, with a focus on invertible maps. A large array of techniques is now available, coming from basic Diophantine geometry, p-adic analysis, dynamical or arithmetic equidistribution theorem. I will focus on a small number of precise results that illustrate well these techniques (including theorems of Dimitrov, of Bell, and of Bilu). Complete proofs will be given. The course will not require any advanced knowledge in algebraic geometry, dynamical systems, or p-adic analysis: the necessary notions will be introduced during the course.

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Prof. Serge Cantat, University of Rennes 1

Note：Please pay attention to the course time. There is no lecture on May3/5/12/26.

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