Title: Hamiltonian Hierarchies and Classical W-algebras

Abstract: The goal of this talk is to look at the connection between integrable systems and W-algebras. We will briefly review two core Hamiltonian hierarchies, the KP hierarchy and its reduction, the n-KdV hierarchy, analyzing them in terms of pseudodifferential operators. Then, we will discuss the fermionic and bosonic formulations of the KP hierarchy, and see how the theory generalizes to the multicomponent case. In the last part of the talk, we will use symplectic reduction as the key tool to construct classical W-algebras and see how they naturally associate to the n-reduced multicomponent KP hierarchy.

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