Quantization of integrable system via deformation quantization of Poisson vertex algebras

Simone Castellan (University of Glasgow)

Tuesday 25th February 16:00-17:00 Maths 311B

Abstract

Following the work of De Sole, Kac, Valeri, classical Hamiltonian PDEs can be formalized using Poisson vertex algebras. This framework is important for two reasons. For start, it gives us new tools to construct and study classical integrable systems. Moreover, Poisson vertex algebras have a well-known canonical quantization, vertex algebras. This suggests a way to quantize a large class of classical integrable systems. In this talk I will explain the classical framework and discuss the ideas for the quantization. No prior knowledge on (Poisson) vertex algebras is assumed.

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