operator algebras and applications to quantum physics

Operator Algebras and Applications to Quantum Physics

Scope of the special session

The theory of operator algebras has deep interrelations with many other mathematical disciplines, so that it provides a unified language allowing a higher level of comprehension. From the start, the theory developed in close relation with the theory of operators, ergodic theory, harmonic analysis, the theory of group representations and quantum physics. More recently, while the structure of the theory was investigated more thoroughly, new connections with other branches of mathematics have emerged, such as the polynomial invariants for topological knots of Vaughan Jones, the free probability of Dan Voiculescu and Alain Connes' noncommutative geometry, which emerges from the confluence of operator algebras and differential geometry.

On the other hand, the applications of operator algebras to quantum physics have always provided an important motivation and have continued to reveal unexpected connections. The relation between the modular structure of von Neumann algebras and the KMS equilibrium condition in statistical mechanics, the structure of superselection sectors and its links with Jones' index theory and with the duality theory of compact groups, and algebraic methods in the construction of QFTs testify to this.

This special session is aimed to continue illustrating part of the current research activity in operator algebras and closely related fields of mathematics, and its applications to other areas, in particular to quantum physics, and to foster interchange and collaboration between people working in these subjects.


  • Daniele Guido (University of Roma - Tor Vergata,  Italy)
  • Fernando Lledó (Charles III University of Madrid and Institute of Mathematical Sciences, Spain) - flledo@math.uc3m.es
  • Gerardo Morsella (University of Roma - Tor Vergata,  Italy)

Abstracts and schedule

Below you can download the schedule and the abstracts of all talks of this special session.


45 minute lectures

  • Giovanni Landi (University of Trieste, Italy)

          On the K-theory and K-homology of quantum lens spaces

  • Gandalf Lechner (University of Leipzig, Germany)

           Operator algebras and the construction of models in quantum field theory

  • Carlos Palazuelos (Complutense University of Madrid, Spain)

           Bell inequalities from a mathematical point of view

  • Francesc Perera (Autonomous University of Barcelona, Spain)

           The Cuntz semigroup and its impact into classification

30 minute lectures

  • Sara Azzali (Istituto Nazionale di Alta Matematica, Italy)

          Two-cocycle twists and Atiyah-Patodi-Singer index theory

  • Fedele Lizzi (University of Naples Federico II, Italy)

           Noncommutative geometry and the standard model of particle physics

  • Pierre Martinetti (University of Naples Federico II, Italy)

           Spectral geometry with a cut-off: topological and metric aspects

  • Enrique Pardo (University of Cádiz, Spain)

          A unified treatment of Katsura and Nekrashevych C*-algebras

  • Juan Manuel Pérez Pardo (Charles III University of Madrid, Spain)

           Quantum symmetries, self-adjoint extensions and reduction theory

  • Mathilde Perrin (Institute of Mathematical Sciences, Madrid, Spain)

           Noncommutative de Leeuw theorems

  • Giuseppe Ruzzi (University of Roma - Tor Vergata, Italy)

           Nets of local C*-algebras and QED representations

  • Ezio Vasselli (University of Rome - La Sapienza, Italy)

           Quantum fields in curved spacetimes and presheaves of superselection structures