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Noncommutative geometry: spaces, bundles and connections

Giovanni Landi and Roberta Iseppi
(University of Trieste/QGM, Aarhus University)
Master Class
17 – 21 September, 2018, in Aud. D3 (1531-215)
In the last years, noncommutative geometry has emerged as a very active field of research. Lying at the intersection between operator algebras and differential geometry, noncommutative geometry has shown itself to be a very effective mathematical framework for crucial results in many areas, from spectral theory, index theorems and foliations to field theories and gravity models in physics. In particular, the relation with physics has been clear from the very beginning: indeed, the Heisenberg uncertainty relations clearly call for the use of noncommutative algebras.  This masterclass aims at giving an introduction to several mathematical results of the field. In particular, we plan to explain how the main idea at the basis of noncommutative geometry of translating geometric objects in algebraic terms, fruitfully applies to concepts such as manifolds, vector bundles and connections.  
Organised by: QGM
Contact person: Roberta Iseppi