Foliated spaces, Tilings and Group actions 2022

This hybrid conference aims to share new ideas on foliated spaces, tilings, group actions and their interrelations. This conference is supported by JSPS Grant-in-Aid for Scientific Research 20K03620.

Date and Place

Date: 17th and 18th December, 2022
Place: Room R101 in Rarcadia (17th Dec.) and Room F205 in Forest House (18th Dec.), Biwako-Kusatsu Campus, Ritsumeikan University Campus map, and Zoom meeting
Registration for on-site participation: Please fill this form. The deadiline is 12th December.
Registration for online participation: Please fill this form. The deadline is 15th December. Please contact hnozawa(at)fc.ritsumei.ac.jp (replace (at) with @) if you have any problem.

Speakers

Ramón Barral Lijó (Ritsumeikan Univ.)
John Hunton (Durham Univ.)
Mitsuaki Kimura (Kyoto Univ.)
Neil Mañibo (Bielefeld Univ.)
Takeo Noda (Toho Univ.)
John Parker (Durham Univ.)
Makoto Sakuma (Osaka Public Univ.)
Norihisa Takahashi (Ritsumeikan Univ.)
Dan Rust (Open Univ.)
Yoshikazu Yamagishi (Ryukoku Univ.)

Programme

(The time is JST=UTC+9)

Saturday 17th December

9:40-10:30	Dan Rust (Zoom)
	Topology of substitution tiling spaces: from finite to compact alphabets
10:50-11:40	Mitsuaki Kimura
	Non-extendability of invariant quasimorphisms and its applications
14:00-14:50	Ramón Barral Lijó
	Dynamical subgroup growth of Cantor actions
15:10-16:00	John Hunton
	Aperiodicity and the Borel Conjecture
	▼Abstract It is easy to show that two homeomorphic spaces are homotopy equivalent. The converse is almost always false. However, the Borel conjecture suggests certain conditions under which two homotopy equivalent spaces are indeed homeomorphic. In this talk I will discuss how the Borel conjecture can be adapted to say something about aperiodic tilings. It is joint work with Alex Clark.
16:20-17:10	Neil Mañibo (Zoom)
	Spectral Theory of Aperiodic Tilings
	▼Abstract In this talk, we will look at aperiodic tilings from a spectral viewpoint, and we will relate characteristics of the diffraction spectrum to properties of the corresponding dynamical system, in particular the corresponding Koopman operator induced by the action. We present some results on spectral characterisation and some open problems. This is based on joint work with Michael Baake, Natalie Frank, Franz Gaehler and Uwe Grimm.

Sunday 18th December

9:40-10:30	Yoshikazu Yamagishi
	Dynamics of the farthest map on the double of a parallelotope
10:50-11:40	Makoto Sakuma
	Two-parabolic-generator subgroups of PSL(2,C)
13:30-14:20	John Parker
	The Poincare polyhedron theorem without convexity
	▼Abstract The Poincare polyhedron theorem gives necessary and sufficient conditions for a polyhedron to tile a space and to be a fundamental domain for the associated group action. It also gives a presentation for the group and the (orbifold) Euler characteristic for the quotient space. It is notoriously difficult to state precisely. In many formulations the polyhedron is assumed to be convex. In this talk I will discuss the theorem and indicate how to remove the hypothesis on convexity.
14:50-15:10	Norihisa Takahashi
	Maximal dihedral actions and their presentations
15:30-16:20	Takeo Noda
	Bar billiards with trajectories tangent to a triangle

Contact

If you have any question, please contact Hiraku Nozawa hnozawa(at)fc.ritsumei.ac.jp (replace (at) with @).