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Graphon Systems and Control Working Group 2019

Peter E. Caines, Rinel Foguen, Shuang Gao, Minyi Huang, Shujun Liu

January 11, 2019 at  2:30 PM
McConnell Engineering Room 437

The first meeting of a weekly working seminar on the theory of graphons and its applications in systems and control theory and related fields will be held 14h30-15h30, Friday, 11th January, 2019, in room 437 of the McConnell Building, McGill University.

A continuum approach to the study of sequences of large, asymptotically infinite graphs or networks emerged relatively recently in the form of the theory of graphons; this theory gives a rigorous formulation of the notion of limits for infinite sequences of networks of increasing size (as measured by the number of nodes) and is developed in the 2012 text by L a´szlo’ Lova´sz. The theory is still undergoing vigorous growth, but it has already revolutionized certain areas of combinatorics and discrete mathematics by connecting them with topology, measure theory and functional analysis. Until now the theory of graphons has mainly been exploited in computer and network science with social and communication networks as prime areas of application (J. Chayes, 2016). However, the application of graphon theory to the analysis and control of networks of dynamical systems and in Mean Field Game theory is now under way (Gao and Caines, 2017, Caines and Huang, 2018).

The purpose of this seminar is for the participants to acquire a working knowledge of graphon theory and to explore its applications in systems and control theory and related domains. The intention is that during the term those who wish to do so will contribute to an ordered set of presentations of material selected by the participants.

All interested are welcome