Mathematics Seminar Series Week 18: Taras Skrypnyk

Join us for this week's Mathematics Essex Seminar, Spring Term 2024. Our MESS talks are open to everyone, and offer a great opportunity to meet new people and join in with our community. 

Taras Skrypnyk (University of Leeds) will present this seminar on Classical non-skew-symmetric r-matrices and integrable spin models.

Abstract

In the present talk we will review a theory of classical non-skew-symmetric non-dynamical r-matrices with spectral parameters and their usage the theory of integrable classical and quantum spin chains. We will explain the relation of these r-matrices with the theory of infinite-dimensional almost-graded Lie algebras with Kostant--Adler decomposition. We will present several classes of examples of such the r-matrices, naturally lying out of the Belavin--Drinfeld classification. In particular, we will present classical r-matrices related to integrable multidimensional tops (Manakov tops). We will also outline a sub-class of the non-skew-symmetric classical r-matrices permitting to construct, except for the linear tensor brackets, also the quadratic tensor brackets that lead to Maillet and reflection equation algebras. We will in details consider Gaudin models with and without external magnetic field and their generalizations based on non-skew-symmetric classical r-matrices. Applications of these models to the problem of isomonodromic deformations and to Kinizhnik--Zamolodchikov--type equations will be briefly discussed.

How to attend

The seminar will be held in STEM 3.1 at 15:00 on Thursday 1 February. It is open to everyone, including the general public. Please contact Dr Dmitry Savostyanov (d.savostyanov@essex.ac.uk) for further information.