Jose Carrillo - Aggregation-Diffusion and Kinetic PDEs for collective behaviour: applications in the sciences

I will present a survey of micro, meso and macroscopic models where repulsion and attraction effects are included through pairwise potentials. I will discuss their interesting mathematical features and applications in mathematical biology and engineering.  Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviours. I will showcase the breadth of possible applications with three different phenomena in applications: segregation, phase transitions and consensus.