![Stable homology of braid groups with symplectic coefficients](/media/cache/video_light/uploads/video/2024-05-07_Petersen.mp4-02e4b37b08b4d31a5bc8706d66c76471-video-339dfc29f5d7136e6a7bcf8ea9ae0a67.jpg)
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Stable homology of braid groups with symplectic coefficients
By Dan Petersen
![Amenability and hyperfiniteness for group actions on trees](/media/cache/video_light/uploads/video/2024-04-25_Spaas.mp4-ab5c65e7dff4e3af6d620c93e1596601-video-72bbba48bae2cf7f296e68672d2ee3a2.jpg)
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Amenability and hyperfiniteness for group actions on trees
By Pieter Spaas
Appears in collection : Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general. Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture. The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve. We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.