My present research develops along the following main lines:

Bundles and gauge groups, mapping spaces and group of self equivalences

Classifying and or enumerate classes of bundles over some classes of spaces and in studying the homotopy type of the gauge groups and or of the classifying space for the gauge groups of classes of bundles. I am also interested in the topology and homotopy of some mapping spaces and in particular in some groups of self equivalences.

papers and preprints

Zeta functions, regularized products, special functions and analytic number theory

Analytic propoerties of the zeta functions associated to some classes of Dirichlet series, with applications in analytic number theory. In particular I am interested in techniques to obtain the main zeta invariants, namely particular values of zeta functions and their derivative. I am also interested in other special functions.

papers and preprints

Reidemeister torsion and analytic torsion

I am investigating the Whitehead torsion and the Reidemeister torsion for some interesting classes of manifolds and pseudomanifolds, in particular spaces with singulrities of conical type.  I also  study analytic torsion and in particular extension of the Cheeger Mueller theorem for manifolds wirh boundary and for manifolds with conical singularities.

papers and preprints

Cellular decomposition and resolution for spherical space forms

We investigate spherical space forms: we introduce a technique that permit to find a cellular decomposition of the covering space equivariant with respect to the group action. As a final result this gives a resolution of the associated spherical space forms group. We applied this method to quaternionic, split metacyclic, and tetrahedral spherical space forms.

papers and preprints

Zeta determinants and relative zeta determinants: application to physics

I am interested in calculations of zeta determiants and relative zeta determinants for functional operators appearing in problems related to geometry and theorethical physics.

paper and preprints

Co workers: S. Albeverio (Bonn, Germany), G. Cognola cognola@science.unitn.it,  M. Crabb (Aberdeen, UK) mcrabb@maths.abdn.ac.uk, L. Hartmann (Sao Carlos, Brazil), O. Manzoli Neto (Sao Paulo, Brazil) ozimneto@icmc.usp.br, R. Piccinini (Milano, Italy) renzo@matapp.unimib.it, D. Lima Gonzalves (Sao Paulo, Brazil) dlgonzal@ime.usp.br, S. Zerbini (Trento, Italy) zerbini@science.unitn.it.

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