Main area of research: Mathematical foundations of quantization (symplectic and Poisson geometry, C*-algebraic formulation of Quantum Mechanics, geometric quantization, systems of imprimitivity).
Other areas of interest:
- In Foundations of Physics: Conceptual comparison between Gauge Theories and General Relativity
- In Mathematics: Application of Category Theory to Physics
- In Philosophy of Physics: The problem of theory change
- In Philosophy of Mathematics: the notion of Identity; Characterization of Abstraction; Mathematical Structuralism; Creativity in Mathematics
As I see it, fundamental research is composed of two different types of activities that should be considered as equally important. On the one hand, there is "conceptual analysis", which aims at clarifying the different notions and objects involved in the various theories, understanding the roots of existing problems, and highlighting the most fundamental ideas that have appeared over the years. On the other hand, there is "technical production", which seeks to find new solutions by, e.g., proposing new models, proving new theorems or developing new mathematical theories. I believe that these two methods—conceptual and technical— must go hand in hand.
The problem is that the actual academic system is governed by a strong emphasis on the production of novelties, and this constitutes a clear hindrance to the development of conceptual analysis. Indeed, this method does not naturally lead to quantitative results nor to practical applications. As a consequence, the current research is overwhelmingly dominated by "technical production", and the deepest ideas get often drowned in a sea of minor results.
In this regard, the existence of independent associations such as the Basic Research Community for Physics appears to me as a crucial step in trying to overturn this dynamic and open new spaces where conceptual analysis can be promoted.