Non standard hierarchical tilings


September 20-22, 2012.

Aim:  The goal of the meeting is to bring together a few experts from C*-algebras, aperiodic tilings, and circle packing to exchange their different perspectives on tilings. The workshop will center around nonstandard hierarchical tilings in dimension 2.
The study of hyperbolic tilings of finite affine type and of Euclidean conformally regular tilings require very different tools than those of the theory of Euclidean aperiodic tilings, and poses challenging questions. For instance, the theory of circle packings introduced by W. Thurston to approximate conformal mappings, and developed in the work of K. Stephenson and P. Bowers, gives a way to define conformally regular tilings of the plane, the Poincaré disk, or the Riemann sphere. These peculiar tilings can have a simple combinatorics, yet cannot be understood using the standard theory of aperiodic tilings. A combinatorial approach allows to define the fundamental tiling objects: a continuous hull, its canonical transversal, and the equivalence relation of orbit equivalence, which is very interesting from a C*-algebraic point of view. The study of such conformal tilings opens new perspectives for hierarchical tilings in dimension 2.

Venue and dates: Centre for Symmetry and Deformation, KU, Copenhagen, September 20-22.

More information:

  • Speakers:

    Natalie Frank (Vassar College, NY , USA)
    Philip L Bowers
     (Florida State University, FL, USA)
    Jean-Marc Gambaudo (University of Nice, France)
    Chaim Goodman-Strauss (University of Arkansas, AR, USA)
    Arnaud Hilion (University of Marseille, France)
    Johannes Kellendonk
    (University of Lyon 1, France)
    Hervé Oyono-Oyono (University of Lorraine - Metz, France)
    Samuel Petite (University of Amiens, France)
    Jean Renault (University of Orléans, France)
    Maria Ramirez-Solano (University of Copenhagen, Denmark)
    Lorenzo Sadun (UT Austin, TX, USA)
    Ken Stephenson
    (University of Tenessee Knoxville, TN, USA)

  • Scientific program

Organizers: Maria Ramirez Solano, Ryszard Nest, Jean Savinien.

Sponsors:   The workshop is cofinanced by Danish and French research institutions: the Center for Symmetry and Deformation, the CNRS (ANR grant SubTile), the LMAM (University of Lorraine - Metz).