About CaLISTA Project

Lie Theory; Cartan Geometry; Quantum Groups; Integrable Systems; Vision

Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications (CaLISTA) COST: CA21109

Areas of Expertise:

  • Mathematics: Lie groups, Lie algebras
  • Mathematics: Geometry
  • Physical Sciences: Mathematical physics

Aims of the Project

Symmetry is a central unifying theme in mathematics and physics.

In this project we focus our attention on symmetries realized through Lie groups and Lie algebras.

In addition to the spectacular achievements in representation theory, and differential geometry, Lie theory is also exceptionally important for the formalization of fundamental physical theories.

CaLISTA aims to advance cutting-edge research in mathematics and physics through a systematic application of the ideas and philosophy of Cartan geometry, a thoroughly Lie theoretic approach to differential geometry.

In addition to making major progress in Cartan geometry itself, CaLISTA aims to develop crucial applications to integrable systems and supersymmetric gauge theories.

Quantum groups and their quantum homogeneous spaces come into the play as a bridge between these topics: quantum groups stem originally from the R-matrix formulation in integrable systems, and their homogeneous spaces offer prototypical examples of noncommutative parabolic geometries.

Parabolic geometry is the first and possibly the most important example of Cartan geometry, and one of the main aims of CaLISTA is to obtain a quantum generalization.

Surprisingly, Lie theory and Cartan geometry play a role in an exciting new interpretation of the differential structure, and related dynamics, of models for popular algorithms of vision like Deep Learning and the more recent Geometric Deep Learning.

CaLISTA aims to investigate and improve on these techniques. CaLISTA will provide essential mathematical models with far-reaching applications, placing Europe among the leading actors in these innovative research areas.


  • Action Chair: Rita Fioresi Italy
  • Action Vice Chair: Karen Strung Czechia
  • Grant Holder Scientific Representative: Réamonn Ó Buachalla Czechia


  • WG1 Leader: Andreas Cap Austria
  • WG2 Leader: Simonetta Abenda Italy
  • WG3 Leader: Réamonn Ó Buachalla Czechia
  • WG4 Leader: Jesús Angulo France
  • WG5 leader: Juraj Tekel Slovakia


  • Science Communication Coordinator: Maria Antonia Lledó Spain
  • Grant Awarding Coordinator: Robert Yuncken France