Noncommutative Geometry Monday

[L. Dabrowski]

Noncommutative Geometry Monday
9 August 2021
in Dubrovin Lecture room 136 (SISSA main building)

with two seminars:

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@ 11:00 Bram Mesland (Leiden)

"The KK-theory perspective on noncommutative geometry"

The observation that the Dirac operator on a spin manifold encodes both
the Riemannian metric as well as the fundamental class in K-homology leads
to the paradigm of noncommutative geometry: the viewpoint that  
spectral triples
generalise Riemannian manifolds. To encode maps between Riemannian manifolds,
one is naturally led to consider the unbounded picture of Kasparov's
KK-theory. In this talk I will explain how smooth cycles in KK-theory give
a natural notion of noncommutative fibration, encoding morphisms  
noncommutative
geometry in manner compatible with index theory. The picture accommodates
for a wide range of examples from geometry, number theory and physics.

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@ 14:30 Francesca Arici (Leiden)

"SU(2)-symmetries and exact sequences of C*-algebras through  
subproduct systems"

Motivated by the study of symmetries of C*-algebras as well as by multivariate
operator theory, in this talk we will introduce the notion
of an SU(2)-equivariant subproduct system of Hilbert spaces. We will describe
their Toeplitz and Cuntz—Pimsner algebras and provide results about their
topological invariants through K(K)-theory.
In particular, we will show that the Toeplitz algebra of the subproduct system
of an irreducible SU(2) representation is equivariantly KK-equivalent
to the algebra of complex numbers, so that the (K)K-theory groups
of the Cuntz—Pimsner algebra can be effectively computed using an  
exact sequence
involving an analogue of the Euler class.
Based on joint work with Jens Kaad (SDU).


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& discussions between and afterwards.