My research activity focuses on the interaction between the topology and the geometry of certain spaces and the analytic properties of a class of differential operators defined on them, the operators of Dirac type. I am particularly interested in considering:

• manifolds with boundary

• Galois coverings of smooth manifolds

• manifolds with non-free actions of compact and non-compact groups

• stratified pseudomanifolds

• foliations 

I use techniques from 

• microlocal analysis

• Riemannian geometry

• algebraic topology (K-Theory, bordism, singular (co)homology, intersection (co)homology)

•  operator algebras

• cyclic (co)homology

• KK-theory