The research carried out in this area has interdisciplinary connections both with other mathematical disciplines and with aspects of computer science, philosophy and education. It is mainly concerned with model theory and its algebraic-geometric applications, non-standard analysis, combinatorics of numbers and set theory.
Current lines of research:
- Model theory, o-minimality, stability, definable groups, Hardy’s fields, derivation, formal series fields, transseries, surreal numbers.
From January - July 2015 Berarducci enjoys the position of visiting Professor at Queen Mary, Univ. of London, thanks to a "Leverhulme Trust" grant (http://www.leverhulme.ac.uk/)
Vincenzo Luca Mantova, Research Fellow, University of Camerino. http://poisson.phc.unipi.it/~mantova/
- O-minimal geometry, with particular regard to the study of real functions appearing naturally in various non-oscillatory problems in dynamic systems and in the theory of numbers. Resolution of singularities for quasi analytical classes and in the application of model theory to real effective geometry.
Derya Ciray, PhD student at the University of Konstanz (Germany)
-PRIN 2012, "Logic, Models and Sets"
National Scientific Coordinator: TOFFALORI Carlo (Univ. of Camerino)
Scientific Coordinator of the Pisa unit: BERARDUCCI Alessandro
Funding body: MIUR
Period: 08/03/2014 - 08/03/2017