Topic: My PhD project focuses on the analysis of singular interacting particle systems, in particular phenomena such as propagation of chaos. The dynamics of these systems are modelled by stochastic differential equations (SDEs) with singular coefficients—for instance,  the drift term in each particle's equation is highly non-smooth.

My primary interest lies in exploring the connections between singular partial differential equations (PDEs) and singular martingale problems, especially within a nonlinear framework. This includes the in-depth study of McKean-Vlasov SDEs.

Motivation: Singular coefficients would account for the singular/irregular nature of the dynamics of each particle, that could be due to exogenous factors (the environment) or endogenous ones (the particles themselves). 

List of Pubblications:

1. Bondi, L., Ferri, J., Giordanengo, N., Venturino, E. (2023). Multiple Predation on Prey Herding and Counteracting the Hunting. In: Mondaini, R.P. (eds) Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics. BIOMAT 2022. Springer, Cham. https://doi.org/10.1007/978-3-031-33050-6_16.

List of Pre-prints:

1. Bondi, L.,  Issoglio, E., Russo, F., (2025). McKean-Vlasov equations with singular coefficients - a review of recent results, Preprint, arXiv:2507.23553 [math.PR] .