Non-commutative Geometry, Index Theory and Mathematical Physics

  • Alain Connes

    Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
  • Ryszard Nest

    University of Copenhagen, Denmark
  • Thomas Schick

    Georg-August-Universität Göttingen, Germany
  • Guoliang Yu

    Texas A&M University, College Station, USA

Abstract

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.

Cite this article

Alain Connes, Ryszard Nest, Thomas Schick, Guoliang Yu, Non-commutative Geometry, Index Theory and Mathematical Physics. Oberwolfach Rep. 15 (2018), no. 3, pp. 1911–1981

DOI 10.4171/OWR/2018/32