A variety of geometric problems give rise to nice dynamical systems.
In the last 40 years, various notions of laminations have appeared as important examples of dynamical systems.
In particular, geodesic surface laminations have a central role in the work of Thurston on surfaces. Bestvina, Feighn and
Handel
defined a more general notion of lamination for free groups by analogy with geodesic laminations of Thurston and used these objects to study subgroup structure of the outer automorphism group Out(F) of the free group.
Ghys defined Riemann surface laminations and explained how spaces of tilings have a
natural lamination structure.
Despite recent progress, many notions of lamination are poorly understood. In particular, it would be nice to understand
(1) laminations associated to systems of partial isometries (in dimension-1, such laminations are
"dual" to group actions on trees) and (2) laminations associated to aperiodic tilings and the symbolic dynamical systems
associated to them.
The aim of this meeting is to gather researchers working on notions of lamination in various contexts:
- Geometric group theory: The laminations appear in the study of Out(F_N). Indeed
this group acts on the Culler Votgmann space, where points are real trees. A dual
lamination is associated to such a tree with an action of free group by isometry.
- Symbolic dynamics: The main object is the subshift--a closed, shift invariant, subset of
bi-infinite sequences over A (where A is a finite "alphabet"). Replacing the integers by more general
group gives a more general class of dynamical systems, whose study is still as its beginning. The general
problem is related to the classical case via colorations of groups, sofic groups, and the
Gottschalk conjecture.
- Tilings: The colorations of the integer lattice in the plane can be seen as a tiling of
the plane by a finite number of tiles. The set of such tilings has a lamination
structure (or solenoid), and laminations have proved very usefull in this context.
Location: CIRM
Dates: 02/04/2012-06/04/2012
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