Geometric Realisation of Spectral Triples

Evelyn Lira-Torres (Queen Mary University of London)

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


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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