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Explore a comprehensive survey of micro, meso, and macroscopic models incorporating repulsion and attraction effects through pairwise potentials in this lecture by José A. Carrillo from Oxford University. Delve into the fascinating mathematical features and applications of these models in mathematical biology and engineering. Examine the crucial role of qualitative properties of local minimizers of interaction energies in understanding complex behaviors. Discover the breadth of potential applications through three distinct phenomena: segregation, phase transitions, and consensus. Gain insights into Aggregation-Diffusion and Kinetic PDEs for collective behavior and their relevance in various scientific fields.
