Boomerang subgroups in lattices of higher Q-rank
Seminar
Speaker
Yair Glasner (Ben-Gurion University of the Negev)
Date
03/06/2026 - 11:30 - 10:30Add to Calendar
2026-06-03 10:30:00
2026-06-03 11:30:00
Boomerang subgroups in lattices of higher Q-rank
Let be a simple, center-free Lie group and a lattice, i.e. a discrete subgroup such that has finite volume. A good example to think of is and . Margulis' celebrated normal subgroup theorem says that, when the real rank of is at least (in the example ) every nontrivial normal subgroup is either finite and central or of finite index. A far reaching generalization by Nevo-Stuck-Zimmer says that, under the same assumptions, every ergodic probability measure preserving (p.m.p) action of (or of ) is either essentially free or supported on an orbit. In a joint work with Waltraud Lederle we generalize this result to a wider class of nonsingular actions which we refer to as "elementwise conservative" actions. We do have to assume a stronger assumption on the lattice, namely that . The proof is surprisingly simple and I will attempt to sketch it in my talk, thus giving in particular a new self-contained proof of the Nevo-Stuck-Zimmer result in the higher -rank case. If time permits, I will briefly discuss works by G-Hartnick-Lederle, Lederle, and Bontemps-Kalma-Lederle, all demonstrating that for free groups elementwise conservative actions are ubiquitous, far beyond the realm of p.m.p actions.
Building 102, Room 4
אוניברסיטת בר-אילן - המחלקה למתמטיקה
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Building 102, Room 4
Abstract
Let 
be a simple, center-free Lie group and 
a lattice, i.e. a discrete subgroup such that 
has finite volume. A good example to think of is  "G = \mathrm{PSL}_n(\mathbb{R})")
and  "\Gamma = \mathrm{PSL}_n(\mathbb{Z})")
. Margulis' celebrated normal subgroup theorem says that, when the real rank of is at least 
(in the example 
) every nontrivial normal subgroup 
is either finite and central or of finite index. A far reaching generalization by Nevo-Stuck-Zimmer says that, under the same assumptions, every ergodic probability measure preserving (p.m.p) action of 
(or of )  "(X,\mathcal{B},\mu,\Gamma)")
is either essentially free or supported on an orbit.
be a simple, center-free Lie group and a lattice, i.e. a discrete subgroup such that has finite volume. A good example to think of is and . Margulis' celebrated normal subgroup theorem says that, when the real rank of is at least (in the example ) every nontrivial normal subgroup is either finite and central or of finite index. A far reaching generalization by Nevo-Stuck-Zimmer says that, under the same assumptions, every ergodic probability measure preserving (p.m.p) action of (or of ) is either essentially free or supported on an orbit. In a joint work with Waltraud Lederle we generalize this result to a wider class of nonsingular actions which we refer to as "elementwise conservative" actions. We do have to assume a stronger assumption on the lattice, namely that %09%5Cge%092 "\mathbb{Q}-rk(\Gamma) \ge 2")
. The proof is surprisingly simple and I will attempt to sketch it in my talk, thus giving in particular a new self-contained proof of the Nevo-Stuck-Zimmer result in the higher 
-rank case.
. The proof is surprisingly simple and I will attempt to sketch it in my talk, thus giving in particular a new self-contained proof of the Nevo-Stuck-Zimmer result in the higher -rank case. If time permits, I will briefly discuss works by G-Hartnick-Lederle, Lederle, and Bontemps-Kalma-Lederle, all demonstrating that for free groups elementwise conservative actions are ubiquitous, far beyond the realm of p.m.p actions.
תאריך עדכון אחרון : 21/10/2026
