On November 21, Professor Diogo Gomes, a leading expert in Applied Mathematics and Computational Science, led a seminar titled 'Monotonicity Methods for Mean Field Games: A Functional Analytic Perspective' at the Faculty of Mathematics and Mechanics, Yerevan State University.

This seminar explored mean field games (MFGs) through the lens of functional analysis, with a particular focus on the role of monotonicity methods in understanding their properties and deriving solutions. The discussion began with an introduction to MFGs as models for large populations of interacting rational agents, illustrating their derivation in the context of deterministic problems. Key questions regarding the existence and uniqueness of MFG solutions were addressed, with special emphasis on the importance of monotonicity operators as a central analytical tool. The seminar established a connection between monotone operators and variational inequalities, demonstrating how the latter framework can be utilized when traditional solution methods fail. Further investigation was made into the use of Hessian operators, Bregman divergence, and regularization techniques for obtaining solutions to MFGs. The presentation then extended the discussion to the Banach space setting, examining monotone operators between a Banach space and its dual, and offering existence theorems and regularization methods tailored to this context. 

The seminar concluded with exploring the concept of weak-strong uniqueness, identifying conditions under which weak and strong solutions of MFGs coincide, and providing a deeper understanding of solution behaviors in large-population settings.

This engaging seminar provided a valuable opportunity for students and professors to interact with the expert and expand their knowledge.