Research topics

My reseach topics focus on several aspects related to the mathematical analysis of Partial Differential Equations arising from Physics, Biology, Ecology and Fluid Mechanics:

• Hydrodynamic and mean field limits: Hyperbolic, parabolic and intermediate scaling limits of kinetic equations towards macroscopic models. Mean field limits of agent-based systems towards kinetic equations. Special attention is given to models arising from collective dynamics, biology and ecology with singular interactions (Cucker–Smale, Kuramoto, etc).

• Long-time behavior: Mathematical analysis of asymptotic dynamics for kinetic equations arising in collective and evolutionary dynamics. Special emphasis is placed to the study of the dynamics of phenotypic traits and other mathematical models for biological propagation phenomena at the mesoscale.

• Modeling cell communication: Modeling and analysis of cytonemes in Drosophila as morphogen carriers, responsible for cell-to-cell transportation of biological information.

• Incompressible fluids: Linked and knotted stream lines and tubes of 3D steady solutions of the Euler equations and stability of generalized Beltrami fields. Vortex sheet solutions to the 2D Euler equations via measured-valued weak solutions in Morrey type spaces.

Click here to access the website of the research group that I belong to, and also here to visit the website of the research unit MNat (Modeling Nature) which I am member of.