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Research talks;Dynamical Systems and Ordinary Differential Equations

In the past few years, conjectures have been made and partial results achieved on unlikely intersections in complex dynamics, following the program initiated by Baker-DeMarco. I will explain their dynamical generalization of the famous André-Oort conjecture on CM points in moduli spaces of abelian varieties. Ghioca, Nguyen, Ye, and myself recently proved the first complete case of this conjecture, for pairs of unicritical polynomials, and I will discuss our result and the connection to invariant subvarieties of $P1 \times P1$, and the structure of the Mandelbrot set. In the past few years, conjectures have been made and partial results achieved on unlikely intersections in complex dynamics, following the program initiated by Baker-DeMarco. I will explain their dynamical generalization of the famous André-Oort conjecture on CM points in moduli spaces of abelian varieties. Ghioca, Nguyen, Ye, and myself recently proved the first complete case of this conjecture, for pairs of unicritical polynomials, and I will ...

37F50 ; 37F05

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- 310 p.
ISBN 978-0-8218-3862-4

Mathematical surveys and monographs , 0118

Localisation : Collection 1er étage

géométrie algébrique arithmétique # surface de Riemann # corps de base # variété modulaire # invariant différentielle # correspondance

14G20 ; 14G35 ; 30F10 ; 53A55 ; 37F05 ; 14L24

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