A case of the dynamical André-Oort conjecture
Also appears in collection : Model Theory, Difference/Differential Equations and Applications / Théorie des modèles, équations différentielles et aux différences et applications
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.
![$k$-sum free sets in $[0,1]$](/media/cache/video_light/uploads/video/2015-09-10_de_Roton-video--19cf70874d3c5af7378c268cab865b06.jpg)
