Global rigidity of actions by higher-rank groups
May 16 to May 20, 2022
American Institute of Mathematics,
San Jose, California
and Zhiren Wang
This workshop will be devoted to actions of higher rank groups such as $SL(n, Z)$, $n \geq
3$ and $Z^d$, $d \geq 2$. The general theme is the global rigidity or
classification of such actions (at times satisfying additional
dynamical hypotheses) up to smooth changes of coordinates. Two major
motivations in this area are the Zimmer program and the Katok-Spatzier
conjecture, which respectively concern the classifications of actions
by lattices in higher rank Lie groups and Anosov actions by higher
rank abelian groups. During the last few years, there have been
numerous breakthroughs for both type of groups, including the proof of
Zimmer's conjecture for $SL(n, Z)$ and cocompact lattices of higher rank
$R$-split simple groups and recent work advancing the classification of
abelian Anosov actions. A large volume of new techniques have appeared
in various directions surrounding these programs, including functional
analysis on groups, homogeneous dynamics, smooth ergodic theory, and
invariant algebraic or geometric structures. Given these developments,
we expect future progress on various global rigidity conjectures.
The goals of the workshop will include:
- Presentations on current state of the art techniques to build
invariant algebraic/geometric structures;
- Construction, classification, and investigation of the properties
of exotic actions;
- Exchange of techniques developed by different research groups with
the goal of developing new collaborations
and making further progress in global rigidity programs.
Material from the workshop
A list of participants.
The workshop schedule.
A list of open problems.