My research focuses on the Mathematics of Collective Dynamics with several lines derived from Physics, Biology, Sociology, and Technology.
• Flocking and alignment models of collective dynamics: Discrete (ODEs), Kinetic (Continuum), and Hydrodynamic (PDEs); Cucker-Smale model, Euler Alignment System, topological interactions
• Fluid dynamics: Compressible Euler equations, Weak-strong uniqueness, measure-valued solutions
• Synchronization models: Classical-Kuramoto model, Quantum Schrödinger-Lohe model, Classical and Quantum Stuart-Landau Oscillators, applications to machine learning and artificial intelligence
• Opinion Dynamics: Discrete and continuous time models of nonlinear consensus dynamics; Degroot model, Friedkin-Johnsen model
• Kinetic theory: Mean field limits, noninterchangeable systems, higher-order interactions