I am a Mathematician specializing in Numerical Analysis, with a strong focus on applied mathematical modeling and structure-preserving numerical methods. My research activity mainly concerns the design and analysis of high-order numerical schemes for differential, integro-differential and integral evolutionary problems, with particular attention to the unconditional preservation of qualitative properties such as positivity, conservation laws, invariants and long-time asymptotic behavior. My work spans the numerical treatment of production–destruction systems, replicator dynamics and non-local models, including unconditionally positive and conservative time discretizations, numerical approaches for optimal control problems and parallel semi-Lagrangian schemes. Furthermore, I have developed mathematical and numerical models for applications in cultural heritage science, addressing data preprocessing strategies for laboratory measurements and inverse problems for model calibration. More recently, my research has expanded toward approximation theory in functional spaces, with the construction and analysis of interpolation and filtered approximation techniques for the numerical solution of Fredholm integral equations.
During my PhD, I focused on dynamically consistent numerical methods for age-of-infection integro-differential epidemic models, developing positivity-preserving discretizations based on non-standard finite differences and convolution quadrature with Gregory weights, and analyzing the long-time behavior of implicit discrete Volterra equations. Earlier, my work addressed PDE-constrained optimal control problems applied to metastatic cancer treatment and numerical methods for data analysis, including the development of a facial recognition algorithm.
