THE RIEMANNIAN GEOMETRY OF A DISCRETIZED CIRCLE AND TORUS

Speaker(s)

ANDRZEJ SITARZ

Affiliation

Uniwersytet Jagielloński

Date

April 7, 2021, 5:15 p.m.

Information about the event

Seminar 2021-04-07 17:15:00

Seminar

North Atlantic Noncommutative Geometry Seminar

---

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

---