My domains of research are optimal control (finite and infinite dimensional), static and dynamic optimization, partial differential equations (finite and infinite dimensional)-linked to optimal control problems-,Mean Field Games and applications to economics and mathematical finance. Below I describe my fields of research in details.
Homogenization and singular perturbations problems for HJ equations, with applications to large deviations of multiscale stochastic volatility models and pricing of out-of-the-money options near maturity; integro-partial differential equations of HJ type related to Lévy processes; finite horizon optimal control problems with discontinuous dynamics and costs.
Mean Field Games (MFGs) with applications to economics:
MFGs with strong aggregation (strong decreasing cost) for aggregation phenomena.
MFGs models in economics with human capital accumulation and spatial spillovers.
Optimal enviromental policies in an heterogeneous world with global awareness.
Mean Field Games in infinite dimension with applications to vintage capital models, systemic risk and production output planning problems
Platform design with dynamic price competition.
Optimal control and optimization in economics:
Habits and demand changes after COVID 19 (i.e. pandemic economy with lockdown of a sector of the economy).
Sparse optimization:
Non convex non smooth sparse optimization, analytical and numerical aspects, with applications in optimal control, reconstruction of images, and fractures mechanics.
Inverse problems in fractures mechanics for the identification of crack by shape optimization techniques.
In my bachelor and master thesis I worked in calculus of variations and optimization. Within this area of research my specific interests have been isoperimetric and Brunn-Minkowski inequalities for variational functionals and quantitative results.