Noncommutative geometry: metric and spectral aspects

Session

30-morning

30 Sept 2022, 09:00

19. Geometrically realised spectral triples and dynamical mass

Shahn Majid

30/09/2022, 09:00

We apply the geometric realisation programme for spectral triples within quantum Riemannian geometry (QRG) to the algebra of 2x2 matrices with a Lorentzian metric to find an S^1 moduli of almost spectral triples where the Dirac operator is not hermitian but has natural hermitian and antihermitian parts (based on joint work with E. Lira-Torres). I will also explain how Kaluza Klein ideas look...

4. Around heat kernel

Bruno Iochum

30/09/2022, 10:00

First, I present a few properties of heat kernel and its trace and then, revisit the way of computing the coefficients of the heat trace asymptotics for a differential operator acting on a fiber bundle over a Riemannian manifold in a way which avoids entering within the pseudodifferential theory.

21. Sequences of Noncommutative Gauge Field Theories on AF-algebras

Thierry Masson

30/09/2022, 11:00

With Gaston Nieuviarts we have built and started to study a new framework to define sequences of Noncommutative Gauge Field Theories (NCGFT) on top of the defining sequence of an AF algebra. The main objective of this construction is to manage the way these NCGFT are related to each other along the sequence. A notion of “compatibility” is then necessary to handle this problem. In my talk, I...

23. Differential nested pairs of quantum homogeneous spaces.

Alessandro Carotenuto

30/09/2022, 12:20

TBA

8. Quantum Kaluza-Klein theory with M_2(C)

Chengcheng Liu

30/09/2022, 12:45

We follow a quantum Kaluza-Klein formulation where we solve for the quantum Riemannian geometry on A = C∞(M) ⊗ M2(C) in terms of classical Riemannian geometry on M, the finite quantum geometry on M2(C) and gauge-field like cross term. We look at how scalar fields on the total space decompose into multiplets of fields in M differing in mass.

22. Spectral triple based Noncommutative Gauge Field Theories on AF-algebras

Gaston Nieuviarts

30/09/2022, 13:10

In the continuity of the presentation made by Thierry Masson, in which the general framework was introduced to define Noncommutative Gauge Field Theories (NCGFT) on top of the sequence of an AF algebra, I will present the part of our work that focuses on the study of these NCGFTs using spectral triples. In particular, I will insist on the
"compatibility" relations on the defining structure of...

3. Spectral and metric aspects of the Dolbeault-Dirac spectral triple on quantum SO(5)/(SO(2)xSO(3)

Elmar Wagner

30/09/2022, 13:35

The Berstein-Gelfand-Gelfand resolution for irreducible quantum flag manifolds gives an algebraic description of the Dolbeault complex of (anti-)holomorphic k-forms by actions of quantum tangent space. Requiring equivariance and compatibility with the real form of the quantum enveloping algebra, there is an essentially unique hermitian metric on the (0,k)-forms given by the Haar state. Using...