My present research develops along the following main lines:
Bundles and gauge groups, mapping spaces and group of self equivalences
I am interested in 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.
co workers: R. Piccinini (Milano, Italy) renzo@matapp.unimib.it, M.
Crabb (Aberdeen, UK) mcrabb@maths.abdn.ac.uk, O. Manzoli Neto
(Sao Paulo, Brazil) ozimneto@icmc.usp.br, D. Lima Gonzalves (Sao Paulo,
Brazil) dlgonzal@ime.usp.br
Zeta functions, regularized products, special functions and analytic
number theory
I am studying 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. We have results for quaternionic
spherical space forms that we aim to extend to other non abelian spherical
space forms. We also studied analytic torsion and in particular extension of
the Cheeger Mueller theorem for manifolds wirh boundary and for manifolds with
conical singularities.
Zeta determinants and relative zeta determinants: application to physics
I am interrested in explicti
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 and S. Zerbini
(Trento, Italy) zerbini@science.unitn.it