Geometric Realisation of Spectral Triples

Evelyn Lira-Torres (Queen Mary University of London)

Thursday 16th November, 2023 16:00-17:00 Maths 311B

Abstract

We will introduce the formalism of Noncommutative Riemannian Geometry over unital algebras based on work by S. Majid and E. Beggs, this will set the basis to introduce a generalisation of A. Connes' Spectral Triples known as Geometric Realisation of Spectral Triples. Given this formalism we will emphasize in a characterisation when the algebra has trivial centre, and when the set of 1-forms \Omega^1 and the 'spinor' bimodule have a central basis. Finally, will show the geometric realisation of spectral triples on the Noncommutative Torus \C_{\theta}[\T^2]. This is joint work with Prof. Shahn Majid in arXiv2208.07821.

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