THE RIEMANNIAN GEOMETRY OF A DISCRETIZED CIRCLE AND TORUS

Prelegent(ci)

ANDRZEJ SITARZ

Afiliacja

Uniwersytet Jagielloński

Termin

7 kwietnia 2021 17:15

Informacje na temat wydarzenia

Seminarium 2021-04-07 17:15:00

Seminarium

North Atlantic Noncommutative Geometry Seminar

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Since the inception of noncommutative geometry, the generalization of Riemannian geometry to the noncommutative setup was a challenge. In this talk, we propose techniques that allow us to provide a complete classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We find general solutions for the torsion-free and metric-compatibility conditions, and show that there are several classes of such solutions containing special ones that are compatible with a metric that gives a Hilbert C*-module structure on the space of one-forms. We compute curvature and scalar curvature for these metrics, and find their continuous limits. Based on the joint paper with A. Bochniak and P. Zalecki: <SIGMA 16 (2020) 143>.

 

https://www.youtube.com/watch?v=aB_1YIv9QJI

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