Current projects:

1. Non commutative geometry and quantum groups - istanton bundles on quantum spheres (together with F. Bonechi and M. Tarlini -  INFN - Firenze).
2. Establish in full generality a quantum duality principle for embeddable quantum homogeneous spaces (together with F. Gavarini , Università di Roma 2 - Tor Vergata);
3. Homogeneous spaces for Nambu-Lie groups and semidirect Nambu structures;
4. Geometrical description of the variety of Lagrangian subalgebras of the Drinfel'd double and connection with the general theory of Poisson homogeneous spaces, variety of Lie bialgebras (together with R. Basili and L. Guerra - Università di Perugia);
5. Orthogonality relations for some classes of basic hypergeometric series that naturally arise in harmonic analysis on quantum homogeneous spaces;
6. Poisson and quantum complex Grassmannians (together with A.J.L. Sheu - University of Kansas).
7. Lie group simmetries of ordinary differential equations  (together with M.C. Nucci - Università di Perugia).

1. Geometry seminar at the Math Department in Perugia: The variety of Lie bialgebras.