## Abstract

The unifying concept behind our project is the use of modern
mathematical techniques to solve various problems
in the frontiers of quantum field theory, enabling us to deal with
questions like the quantization of space time,
the issue of renormalization, algebraic and topological quantum field theories.
Geometry and symmetry have always been a basic tool of scientific
investigations. Their applications to modern
physics, and quantum field theory in particular, have been immensely
successful. The deformations of geometry and
symmetries are at the basis of quantization and might be a key ingredient for further developments.
The aim of our group is the use and developments of mathematical tools
for the study of advanced quantum with a view to the applications mainly to quantum
gravity and quantum spacetime, field theory,
physics beyond the standard model, string theory and noncommutative
geometry, but also more traditional particle phenomenology,
condensed matter and application to biological systems.

The generalizations of geometry in which we work have had already an
impact on the research in particle physics
and gravitation. The approach to the standard model based on
noncommutative geometry and the
standard model, although still speculative, is getting closer to
phenomenology, the Higgs and neutrinos.
Topological and deformed field theories can be used for quantum
gravity, and geometry is once again a
useful tool for the understanding of the intricacies of renormalization.