Graduate seminars on operator algebras

Progress

Oct 06 by Yamashita
- Thom isomorphism in K-theory
- de Rham homology
- Thom isomorphism in cohomology
- Cyclic cohomology
Oct 11 by Tanimoto
- Canonical weight on left Hilbert algebra
- KMS condition
Oct 13 by Zhang
- Trace on nov Neumann algebra
- Existence of sufficiently many tracial states for finite von Neumann algebras
- Central conditional expectation for finite von Neumann algebras
Oct 18 by Sakiyama
- Ideals of an AF C*-algebra and its ordered K₀-group
- Traces on algebras and K-groups
- Projectionless simple algebra a la Blackadar
Oct 20 by Yamashita
- Toeplitz cyclic 1-cocycle and Bott element
- Smooth / continuous algebra of foliation
- Topological index map for foliation
- Pairing of topological index and holonomy invariant transverse density
- Secondary characteristic classes of codimension 1 foliation
Oct 25 by Mimura
- Toeplitz algebra
- Structure of isometries on Hilbert spaces
- Weighted unilateral shift
- Bunce-Deddens algebra
Oct 27 by Yamashita
- Classical interpretation of Godbillon-Vey
- Modular automorphism and fiber translation
Oct 27 by Zhang
- Semifinite normal trace on semifinite von Neumann algebras
Nov 1 by Tanimoto
- Holomorphic functional calculus of unbounded positive self adjoint operators
- Application to the modular operator of left Hilbert algebra
- Construction of Tomita algebra
Nov 8 by Sakiyama
- Structure of Bunce-Deddens algebra
- Cuntz algebra
- Expectation of Cuntz algebra onto UHF algebra
Nov 15 by Yamashita
- Comparison of transverse 2-jet bundle and 1-jet bundle
- Cyclic 1-trace corresponding to Godbillon-Vey class
- Invariant probability measure on the flow of weights
- Codimension 1 transverse Hopf algebra H₁
Nov 17 by Zhang
- Pairing between noncommutative L¹ and L^∞ for semifinite von Neumann algebras
- Standard representation of semifinite von Neumann algebras
Nov 29 by Mimura
- Simplicity of Cuntz algebras
- Infinite, properly infinite C*-algebras
- Characterization of purely infinite simple algebras
Dec 1 by Ogawa
- Commutant and type classification of von Neumann algebras
- Tensor product and type classification of von Neumann algebras
- Noncommutative Radon-Nykodim for semifinite normal traces
Dec 8 by Yamashita
- Bost-Connes system as moduli of Q-lattices in R
- Moduli of Q-lattices in C
- Modular functions and GL₂(Q) action
- Action of the Hopf algebra H₁
Dec 13 by Sakiyama
- Extension group of Cuntz algebras
- Classification of Cuntz algebras
- Real rank 0 algebras
Dec 15 by Zhang
- Spatial structure of semifinite von Neumann algebras
- Coupling function for "spatially finite" von Neumann algebras
Dec 20 by Mimura
- Real rank 0 algebras
- AT algebras
Dec 22 by Ogawa
- Extended center valued trace on semifinite von Neumann algebras
- Unitary involution and unitary equivalence of von Neumann algebras
Jan 12 by Yamashita
- The action of the Hopf algebra H₁ on the modular Hecke algebra M ⋊ GL₂⁺Q
- Scharzian cocycle is inner
Jan 17 by Tanimoto
- Arveson spectrum of automorphism groups of von Neumann algebras
- Connes spectrum of automorphism groups
Jan 19 by Ogawa
- Comparison of crossed product with different spatial realizations
- Group-space construction of type II₁, II_∞, III factors
Jan 19 by Yamashita
- Poisson bracket on the transverse 1-jet bundle
- Extension of the Rankin-Cohen brackets to the crossed product
Jan 24 by Sakiyama
- Irrational rotation algebra A_θ
- Embedding of A_θ into an AF algebra

Graduate seminars on operator algebras (winter 2006)

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Progress