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Explore advanced mathematical modeling of collective motion phenomena through the lens of congestion principles in this comprehensive lecture by Bertrand Maury from Laboratoire de Mathématiques d'Orsay. Delve into crowd motion models that assume individual entities have personal tendencies counteracted by the presence of others, moving beyond traditional swarming and mimetism approaches. Examine how information propagates through populations and discover gradient flow models built on the principle that populations minimize global dissatisfaction while incorporating congestion constraints. Learn about microscopic modeling approaches and their macroscopic extensions based on optimal transportation principles, understanding how classical mechanics principles including action-and-reaction symmetry can be modified to create more realistic interaction models with asymmetric individual interactions. Gain insights into the mathematical frameworks that describe how congestion fundamentally shapes collective behavior in complex systems.
