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Extra Form
Lecturer Jean V. Bellissard
Dept. Georgia Institute of Technology, School of Mathematics and School of Physics
date Mar 20, 2014

After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finite Local Complexity" or of "Repetitivity" will be interpreted in terms of the tiling space. The special case of quasicrystal will be described. In the second part of the talk, various tools will be introduced to compute the topological invariants of the tiling space. First the tiling space will be seen as an inverse limit of compact branched oriented manifolds (the Anderson-Putnam complex). Then various cohomologies will be defined on the tiling space giving rise to isomorphic cohomology groups. As applications, the "Gap Labeling Theorem" will be described, and some results for the main quasicrystal and simple tilings will be given.


Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Connes's Embedding Conjecture and its equivalent file RIMS Narutaka Ozawa
Math Colloquia Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
Math Colloquia Unprojection file University of Warwick / 서강대 Miles Reid
Math Colloquia A new view of Fokker-Planck equations in finite and Infinite dimensional spaces file Bielefeld Univ./Purdue Univ. Michael Roeckner
Math Colloquia Convex and non-convex optimization methods in image processing file Hong Kong Baptist University Michael Ng
Math Colloquia Sheaf quantization of Hamiltonian isotopies and non-displacability problems file Kyoto Univ./서울대학교 Masaki Kashiwara
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
Math Colloquia Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
Math Colloquia The classification of fusion categories and operator algebras file Kyoto University Masaki Izumi
Math Colloquia Conservation laws and differential geometry file Univ. of Wisconsin Marshall Slemrod
Math Colloquia Quasi-homomorphisms into non-commutative groups file Kyoto Univ. Koji Fujiwara
Math Colloquia Number theoretic results in a family file Univ. of Toronto / KIAS Kim, Henry
Math Colloquia A-infinity functor and topological field theory file Simons Center for Geometry and Physics Kenji Fukaya
Math Colloquia Deformation spaces of Kleinian groups and beyond file Osaka University Kenichi Ohshika
Math Colloquia Analytic torsion and mirror symmetry file Kyoto University Ken-ichi Yoshikawa
Math Colloquia Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields file Univ. Bremen Keivan Mallahi-Karai
Math Colloquia Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Harmonic Analysis (Kalachand Shuin) file BK21 Kalachand Shuin
Math Colloquia Noncommutative Surfaces file 서강대학교 Jens Hoppe
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