May 27 – 31, 2024
Institut Henri Poincaré
Europe/Paris timezone
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Zimmer's conjecture for non-split semisimple Lie groups

May 27, 2024, 9:30 AM
Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Amphithéâtre Hermite / Darboux

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris


Zhiyuan Zhang (Imperial College)


Zimmer conjectures that a higher rank lattice in a semisimple Lie group cannot have essentially non-trivial action on manifolds with dimension smaller than certain quantity related to the Lie group. This conjecture is proved in many cases by Aaron Brown, David Fisher and Sebastian Hurtado. Their result provides sharp dimension bounds for real split semisimple real Lie groups but not sharp otherwise. We discuss a recent generalisation of their result with sharp bound to some other (non-real split) semisimple Lie groups. This is a joint work with Jinpeng An and Aaron Brown.

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