Nowadays, most of Symplectic topology and Gauge theory are based on a very diverse and profound set of Floer theories, which are themselves derived from a rich and complex corpus of moduli spaces. In this school, which is part of the Jean Morlet Chair semester granted to François Lalonde, some theories that have all followed the Floer theory, but in contexts that are far more general or in contexts that seem a priori radically different will be the main focus. Such theories are : the Floer theory itself, the Fukaya-Oh-Ohta-Ono theory, the Cornea-Lalonde Cluster theory, the Embedded contact homology, the Symplectic field theory, the cobordisms and rigidity of Lagrangian submanifolds theory developed by Biran-Cornea etc.
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