1. My main research interest regards Model Theory and its applications to the algebraic investigation of structures. The relationship between Model Theory and Algebra (and Algebraic Geometry) dates back at least to the fifties and Abraham Robinson and is growing in the last decades. In fact the abstract model theoretic treatment of relevant notions such as classification, independence, dimension can produce and is producing several direct applications to Algebra. The specific setting of my own research is Model Theory of Modules, a setting where various concepts suggested by Mathematical Logic – like the lattice of pp-formulas, or Ziegler topology, or some notions of dimnesion – are becoming usual tools in the algebraic investigation. Most of my publications and my invited lectures refer to this matter. I wrote two books with Annalisa Marcja on Model Theory.

Coworkers: S. Baratella (Trento), I. Herzog (Ohio State), A. Marcja (Florence), M. Prest (Manchester), G. Puninski (Manchester), V. Puninskaya (Camerino-Moscow).

My coworkers in Camerino include: S. Leonesi (PhD), S. L’Innocente (PhD)

2. A recent research interest is that linking Number Theory, Computability and Computational Complexity. An underlying common matter connecting these areas is, for instance, Public Key Cryptography. For, since its beginning in the last seventies, one realized that notions and techniques from Complexity and Number Theory can produce safe and reliable cryptographic protocols in electronic commerce, digital authentication and so on. Computational Complexity can also determine the effective cost (in time, memory, or money) of these procedures. In this setting I wrote a book (in cooperation) and several surveys. Also, I edited some special issues of international journals such as Task and Mathematical Structures in Computer Science.

My coworker in Camerino is P. Cintioli (assistant professor).

3. Finally, I matter that is intriguing me in the latest years is that of popularizing Mathematics, in particular Mathematical Logic, its development in the last century, its role in Mathematics and its contributionun to Mathematics. In this framework my interests include the birth of Set Theory and Cantor theory of transfinite numbers, Hilbert’s Program, Gödel’s Incompleteness Theorems, the beginning of Computability Theory, and so on. I devoted 3 books and various expository papers to these matters.

Cooperations: Angelo Guerraggio and the Pristem group of the Bocconi University.