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