Research

Broadly speaking, my research interests lie in the field of differential geometry and its interplay with mathematical physics.

I work with higher geometry methods in multisymplectic geometry and, most of all, I am interested in structures “up to homotopies” inspired by geometry and mechanics.

My research project focuses on the notions of L_∞ algebra of observables and homotopy comomentum maps. These are the higher analogues of smooth observables and the ordinary comoment map in the context of n-plectic geometry. My key results are related to the explicit construction of non-trivial instances of these objects with possible application in different areas of mathematics (e.g. knot theory) and physics (e.g. hydrodynamics).

Nowadays, I am investigating the notion of gauge transformations and (symplectic) reduction in the context of multisymplectic geometry.

A deep motivation for pursuing this line of research can be tracked in my interest in understanding the axiomatic and geometric foundation of classical field theories (i.e. mechanical systems with infinite and continuous degrees of freedom). In this perspective, I am always interested in expanding my knowledge both in the pure direction (homotopical algebra, higher categories) than in the applied direction (symplectic integrators, numerical simulations).