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Oberwolfach Reports

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Volume 15, Issue 3, 2018, pp. 1911–1981
DOI: 10.4171/OWR/2018/32

Published online: 2019-08-26

Non-commutative Geometry, Index Theory and Mathematical Physics

Alain Connes[1], Ryszard Nest[2], Thomas Schick[3] and Guoliang Yu[4]

(1) Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
(2) University of Copenhagen, Denmark
(3) Georg-August-Universität Göttingen, Germany
(4) Texas A&M University, College Station, USA

Noncommutative geometry today is a new but mature branch of mathematics shedding light on many other areas from number theory to operator algebras. In the 2018 meeting two of these connections were high-lighted. For once, the applications to mathematical physics, in particular quantum field theory. Indeed, it was quantum theory which told us first that the world on small scales inherently is noncommutative. The second connection was to index theory with its applications in differential geometry. Here, non-commutative geometry provides the fine tools ot obtain higher information.

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Connes Alain, Nest Ryszard, Schick Thomas, Yu Guoliang: Non-commutative Geometry, Index Theory and Mathematical Physics. Oberwolfach Rep. 15 (2018), 1911-1981. doi: 10.4171/OWR/2018/32