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Noncommutative Geometry and Optimal Transport

Noncommutative Geometry and Optimal Transport

          
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About the Book

This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 214, in Besancon, France. The distance formula in noncommutative geometry was introduced by Connes at the end of the 198s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 199s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffelsobservation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.

About the Author

Pierre Martinetti, Universita di Genova, Italy. Jean-Christophe Wallet, CNRS, Universite Paris-Sud 11, Orsay, France.


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Product Details
  • ISBN-13: 9781470422974
  • Publisher: American Mathematical Society
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 222
  • Series Title: Contemporary Mathematics
  • Weight: 3958 gr
  • ISBN-10: 1470422972
  • Publisher Date: 30 Oct 2016
  • Edition: Contemporary Mathematics
  • Language: English
  • Returnable: Y
  • Spine Width: mm
  • Width: 152 mm


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