We will show the quantum Riemannian geometry on $M_2 (\mathbb{C})$ based on the formalism of Noncommutative Riemannian Geometry over unital algebras done by S. Majid and E. Beggs. We will then introduce what is the quantum realisation of spectral triples using $M_2 (\mathbb{C})$ as example. We will show the case when we are forced to a flat quantum Levi-Civita connection and a even quantum geometrically realised spectral triple. This is joint work with S. Majid arXiv2208.07821.

Bio: Evelyn Lira-Torres is a Mexican mathematician. Lira-Torres is concluding her doctorate degree in Mathematics at Queen Mary University of London-UK under the supervision of Prof. Shahn Majid, before that she got her degree in mathematics at UNAM-Mexico. Her research interests are mostly on noncommutative geometry, operator algebras, topology and mathematical physics.