Rigidity, Dynamics, and Group Actions (05w5029)
David Fisher (Lehman College - CUNY)
Elon Lindenstrauss (Hebrew University)
Dave Morris (University of Lethbridge)
Ralf Spatzier (University of Michigan)
- local and global rigidity of actions,
- low-dimensional actions of large groups,
- orbit-equivalence rigidity, and
- invariant measures for actions on homogeneous spaces.
The foremost experts in each area will report on recent progress.
The most recent meetings in the field were a special semester (on a much broader collection of topics) at the Newton Institute during Spring 2000, a one-week workshop at ETH-Zurich in June, 2002, and a one-week meeting (basically on a subset of D) at the American Institute of Mathematics in June, 2004. There have been several important new developments already since the Zurich meeting.
Another goal is to encourage the transfer of techniques between the areas. Researchers in each of the areas have recently borrowed ideas from other areas of mathematics, but these ideas have not yet been applied more broadly. Illustrative examples include:
- the use by Fisher and Margulis of some ideas from KAM theory,
- the use of both symplectic topology by Polterovich and (generalizations
of) Thurston normal form theory by Franks and Handel for recent
developments on surface actions,
- the use of ideas from operator algebras in recent work of Gaboriau and
- close connections with analytic number theory in the works of Einsiedler,
Katok and Lindenstrauss.
Given the close connections between the fields, it seems likely that these and other ideas are relevant to more than one of the topics.