Quantum Groups and Noncommutative Geometry

Research topics

Research Plan

The research plans for next few years concentrate on two main lines.

  1. The construction of instantons and their moduli spaces on quantum spaces, and their applications. A first task is to complete the study of quantum moduli spaces for instantons on quantum S4. In the longer perspective this serves to valuate the possibility to set up the stage for a generic quantum 4-manifold, in view of non-commutative generalizations of the Donaldson theorem.
  2. The study of the differential structure (Riemannian metric and spin) on quantum spaces, and their applications. Firstly, we intend to proceed with the study of the relations between the quantum group deformations and the Connes spectral triples.


Noncommutative geometry of quantum groups and their homogeneous spaces