Functional Analysis and Differential Geometry
The research activity of the group focuses on certain aspects of functional and harmonic analysis, differential geometry and on their interactions.
As for the more analytical aspects, several classes of differential and integral operators on Euclidean spaces, Lie groups, Riemannian and subRiemannian manifolds and graphs are considered. Furthermore, definitions and properties of various functional spaces in such contexts are also studied.
Analytical methods are fundamental in the study of various geometric problems, in particular of those that arise in the context of geometric flows or of variational problems concerning the curvatures. On the other hand, geometrical method can be applied in the analytical context, for instance in the study of symmetries and conservation laws for systems of partial differential equations. Beside the classical approach, based on the continuous model, the same problems are investigated in the discrete context.
Specifically, the research topics of the group are the following: