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.

첨부 '1'
  1. Green’s function for initial-boundary value problem

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

  3. On the distributions of partition ranks and cranks

  4. Q-curvature in conformal geometry

  5. Zeros of the derivatives of the Riemann zeta function

  6. Geometry, algebra and computation in moduli theory

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

  8. High dimensional nonlinear dynamics

  9. What is model theory?

  10. Essential dimension of simple algebras

  11. Restriction theorems for real and complex curves

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

  13. Deformation spaces of Kleinian groups and beyond

  14. Idempotents and topologies

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

  16. Existence of positive solutions for φ-Laplacian systems

  17. Riemann-Hilbert correspondence for irregular holonomic D-modules

  18. Normal form reduction for unconditional well-posedness of canonical dispersive equations

  19. Random conformal geometry of Coulomb gas formalism

  20. Categorification of Donaldson-Thomas invariants

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 Next
/ 11