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Extra Form
강연자 Jean V. Bellissard
소속 Georgia Institute of Technology, School of Mathematics and School of Physics
date 2014-03-20

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.


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첨부 '1'
  1. Regularity of solutions of Hamilton-Jacobi equation on a domain

  2. What is Weak KAM Theory?

  3. 정년퇴임 기념강연: 회고

  4. <학부생을 위한 강연> 사색 정리를 포함하는 Hadwiger의 추측의 변형에 관하여

  5. The classification of fusion categories and operator algebras

  6. Green’s function for initial-boundary value problem

  7. Mechanization of proof: from 4-Color theorem to compiler verification

  8. On the distributions of partition ranks and cranks

  9. Q-curvature in conformal geometry

  10. Zeros of the derivatives of the Riemann zeta function

  11. Geometry, algebra and computation in moduli theory

  12. Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology

  13. High dimensional nonlinear dynamics

  14. What is model theory?

  15. Essential dimension of simple algebras

  16. Restriction theorems for real and complex curves

  17. Recommendation system and matrix completion: SVD and its applications (학부생을 위한 강연)

  18. Deformation spaces of Kleinian groups and beyond

  19. Idempotents and topologies

  20. Recent progress on the Brascamp-Lieb inequality and applications

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