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Global rigidity of actions by higher-rank groups

July 12 to July 16, 2021

at the

American Institute of Mathematics, San Jose, California

organized by

Aaron Brown, David Fisher, Ralf Spatzier, and Zhiren Wang

This workshop, sponsored by AIM and the NSF, 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.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than January 12, 2021. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.

For more information email workshops@aimath.org


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