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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.
- FILE
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