Zimmer's conjecture for nonsplit semisimple groups

[Math. Dept.]

May 16, 2019  11:00-12:00

W303  School of Mathematics





Zimmer's conjecture states that a lattice in a higher rank real semisimple Lie group cannot act nontrivially on a compact manifold of dimension less than a constant given explicitly by the group. A breakthrough was made recently by Aaron Brown, David Fisher and Sebastian Hurtado. They proved the conjecture for cocompact lattices in split semisimple groups. For nonsplit groups, they also established a weaker result in which the dimension of the manifold is assumed to be less than a smaller constant. In this talk, we discuss the proof of Zimmer's conjecture for cocompact lattices in some nonsplit groups, including all complex semisimple groups and many noncomplex nonsplit almost-simple groups. This is a joint work with Aaron Brown and Zhiyuan Zhang.


Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University