Noncommutative Geometry and Physics 3: 1 (Keio COE Lecture by Giuseppe Dito,Motoko Kotani,Yoshiaki Maeda,Hitoshi

By Giuseppe Dito,Motoko Kotani,Yoshiaki Maeda,Hitoshi Moriyoshi,Toshikazu Natsume,Satoshi Watamura

Noncommutative differential geometry is a singular method of geometry, aimed partially at purposes in physics. It was once based within the early eighties by way of the 1982 Fields Medalist Alain Connes at the foundation of his primary works in operator algebras. it really is now a truly lively department of arithmetic with real and capability purposes to various domain names in physics starting from sturdy country to quantization of gravity. the tactic is to formulate ordinary differential geometry in a a little bit strange demeanour, utilizing particularly operator algebras and similar thoughts, in order to manage to plug in noncommutativity in a common approach. Algebraic instruments equivalent to K-theory and cyclic cohomology and homology play an incredible function during this box. it's an incredible subject either for arithmetic and physics.

Contents:

  • K-Theory and D-Branes, Shonan:
    • The neighborhood Index formulation in Noncommutative Geometry Revisited (Alan L Carey, John Phillips, Adam Rennie and Fedor A Sukochev)
    • Semi-Finite Noncommutative Geometry and a few functions (Alan L Carey, John Phillips and Adam Rennie)
    • Generalized Geometries in String Compactification situations (Tetsuji Kimura)
    • What ensue to Gauge Theories lower than Noncommutative Deformation? (Akifumi Sako)
    • D-Branes and Bivariant K-Theory (Richard J Szabo)
    • Two-Sided Bar buildings for Partial Monoids and purposes to K-Homology concept (Dai Tamaki)
    • Twisting Segal's K-Homology thought (Dai Tamaki)
    • Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular types (Kazufumi Kimoto and Masato Wakayama)
    • Coarse Embeddings and better Index difficulties for Expanders (Qin Wang)
  • Deformation Quantization and Noncommutative Geometry, RIMS:
    • Enriched Fell Bundles and Spaceoids (Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul)
    • Weyl personality formulation in KK-Theory (Jonathan Block and Nigel Higson)
    • Recent Advances within the learn of the Equivariant Brauer workforce (Peter Bouwknegt, Alan Carey and Rishni Ratnam)
    • Entire Cyclic Cohomology of Noncommutative Manifolds (Katsutoshi Kawashima)
    • Geometry of Quantum Projective areas (Francesco D'Andrea and Giovanni Landi)
    • On Yang–Mills thought for Quantum Heisenberg Manifolds (Hyun Ho Lee)
    • Dilatational Equivalence sessions and Novikov–Shubin variety Capacities of teams, and Random Walks (Shin-ichi Oguni)
    • Deformation Quantization of Gauge conception in ℝ4 and U(1) Instanton difficulties (Yoshiaki Maeda and Akifumi Sako)
    • Dualities in box Theories and the function of K-Theory (Jonathan Rosenberg)
    • Dualities in box Theories and the position of K-Theory (Jonathan Rosenberg)

Readership: Researchers and graduate scholars in Mathematical Physics and utilized Mathematics.

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