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FIELD
Mathematics
DATE
Dec 08 (Fri), 2023
TIME
10:30 ~ 11:30
PLACE
8406
SPEAKER
Carpentier, Sylvain
HOST
Lee, Sin-Myung
INSTITUTE
QSMS, Seoul National University
TITLE
Algebraic structures underlying integrability
ABSTRACT
In the first part of this talk, we review the theory of classical integrable systems through the scope of Lax operators. We show how these differential operators encode the symmetries, Hamiltonian structures and solutions of the integrable systems. In one spatial dimension, integrable systems are reductions of the so-called Kadomstev Petviashvili hierarchy. In particular, based on the work of De sole Kac and Valeri, we explain how rational Lax operators can be used to construct integrable hierarchies on classical W algebras, as well as provide their explicit generators and relations. Finally we show how to quantize integrable systems via a free associative lift of the Lax operator. This new method of quantization is a joint work with A. Mikhailov and J.P. Wang.
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