eBook ISBN:  9781470435608 
Product Code:  CONM/676.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470435608 
Product Code:  CONM/676.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 676; 2016; 223 ppMSC: Primary 00; 46; 58; 53
This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 2014, in Besançon, France.
The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. 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 1990s, 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, Rieffel's observation 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.
ReadershipGraduate students and research mathematicians interested in noncommutative geometry.

Table of Contents

Articles

Pierre Martinetti — From Monge to Higgs: a survey of distance computations in noncommutative geometry

Frédéric Latrémolière — Quantum Metric Spaces and the GromovHausdorff Propinquity

Michel DuboisViolette — Lectures on the classical moment problem and its noncommutative generalization

Nicolas Franco and JeanChristophe Wallet — Metrics and causality on Moyal planes

Francesco D’Andrea — Pythagoras Theorem in noncommutative geometry

Mijail Guillemard — An Overview of Groupoid Crossed Products in Dynamical Systems


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This volume contains the proceedings of the Workshop on Noncommutative Geometry and Optimal Transport, held on November 27, 2014, in Besançon, France.
The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. 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 1990s, 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, Rieffel's observation 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.
Graduate students and research mathematicians interested in noncommutative geometry.

Articles

Pierre Martinetti — From Monge to Higgs: a survey of distance computations in noncommutative geometry

Frédéric Latrémolière — Quantum Metric Spaces and the GromovHausdorff Propinquity

Michel DuboisViolette — Lectures on the classical moment problem and its noncommutative generalization

Nicolas Franco and JeanChristophe Wallet — Metrics and causality on Moyal planes

Francesco D’Andrea — Pythagoras Theorem in noncommutative geometry

Mijail Guillemard — An Overview of Groupoid Crossed Products in Dynamical Systems