Noncommutative geometry
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https://openscholarship.wustl.edu/iwota2016/special/NCgeo
Recent Events in Noncommutative geometry
enus
Tue, 25 Sep 2018 18:31:39 PDT
3600

TBA
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/7
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/7
Fri, 22 Jul 2016 15:30:00 PDT
TBA
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YiJun Yao

Brylinski's sheaf complex for proper Lie groupoids
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/5
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/5
Fri, 22 Jul 2016 15:00:00 PDT
In this talk we generalize Brylinski's sheaf complex from Gmanifolds to proper Lie groupoids. Moreover, we explain the connection between this complex and the cyclic homology theory of the convolution algebra of the underlying proper Lie groupoid. The talk is on joint work with H. Posthuma and X. Tang.
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Markus Pflaum

Quantitative $K$theory for $SQ_p$algebras
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/4
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/4
Fri, 22 Jul 2016 16:00:00 PDT
Quantitative (or controlled) $K$theory for $C^*$algebras was introduced by Guoliang Yu in his work on the Novikov conjecture for groups with finite asymptotic dimension, and was later expanded into a general theory, with further applications, by Yu together with HervĂ© OyonoOyono. Motivated by investigations of the $L_p$ BaumConnes conjecture, we will describe an analogous framework of quantitative $K$theory that applies to algebras of bounded linear operators on subquotients of $L_p$ spaces.
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Yeong Chyuan Chung

Quantizations and index theory
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/3
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/3
Fri, 22 Jul 2016 14:30:00 PDT
One way to describe succinctly local index theory on closed spin manifolds could be the following slogan of Quillen : Dirac operators are a "quantization" of connections, and index theory is a "quantization" of the Chern character. For non necessarily spin manifolds, pseudodifferential operators and their symbolic calculus play a crucial role in the original proofs of the index theorem. However, symbols may also be viewed as a deformation quantization of functions on the cotangent bundle, which has led to other fruitful approaches to index theory through a "quantization" process. Methods used in these two different quantization pictures do not seem to be quite related a priori. The upshot of the talk will be to see that these different theories might have more to say to each other, and that far reaching index problems may be solved very directly from such an interaction.
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Rudy Rodsphon

The slice property and equalizers of diagrams of C*algebras.
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/2
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/2
Fri, 22 Jul 2016 17:30:00 PDT
Let $A$ and $B$ be two C$\sp*$algebras. For any C$\sp*$subalgebra $ D$ of $B$ which is equalizer defined by *homomorphism $\phi_1$, $\phi_2$ : $ B\longright C $ where $C$ is an other C$\sp*$algebra. $( A, D. B)$ has the slice property if and only if the tensor product spatial $A\otimes D$ is an equalizer defined by the canonical *homomorphism $id:_A \otimes \phi_1$ and $ id_A \otimes \phi_2$.
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Rachid El Harti

Iterated Joins of Compact Groups
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/1
https://openscholarship.wustl.edu/iwota2016/special/NCgeo/1
Fri, 22 Jul 2016 17:00:00 PDT
(Joint work with Alexandru Chirvasitu.) The BorsukUlam theorem in algebraic topology indicates restrictions for equivariant maps between spheres; in particular, there is no odd map from a sphere to another sphere of lower dimension. This idea may be generalized greatly in both the topological and operator algebraic settings for actions of compact (quantum) groups, leading to the the noncommutative BorsukUlam conjectures of Baum, Dabrowski, and Hajac. I will present our recent progress (both positive and negative) toward resolving these conjectures using properties of iterated compact group joins.
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Benjamin Passer