These results were achieved in collaboration with Andrea Raimondo and Daniele Valeri in the recent papers http://arxiv.org/abs/1501.07421, http://arxiv.org/abs/1511.00895
The meeting will take place at the School of Mathematics, Statistics and Actuarial Science, University of Kent on the 9th December 2015.
It is supported by the Mathematical and Theoretical Physics group of the Institute of Physics.
| 10:30 | Coffee | ||
| 11.00 | Davide Masoero (Lisboa) | Bethe Ansatz and the spectral theory of affine Lie algebra-valued connections | |
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The ODE/IM correspondence is a rich and surprising link between the spectral theory of classical Lax operators and integrable quantum field theories. It dates back to the work of Dorey, Dunning and Tateo, and Bazhanov, Lukyanov and Zamolodchikov , who proved that the spectral determinants of particular Schroedinger operators coincide with the eigenvalues of the Q operator of the quantum KdV model.
In this talk we consider a class of affine Lie algebra-valued connections (Drinfeld-Sokolov operators) and we construct solutions of the Bethe Ansatz equations of the quantum g-KdV model - for any simple Lie algebra g. The techniques used for the proof include the representation theory of simple Lie algebras and affine Kac-Moody algebras, as well as the asymptotic theory of linear ODEs in the complex plane.
These results were achieved in collaboration with Andrea Raimondo and Daniele Valeri in the recent papers http://arxiv.org/abs/1501.07421, http://arxiv.org/abs/1511.00895 |
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| 12.00 | Lunch in the Gulbenkian cafe | ||
| Woolf Seminar Room 4 | |||
| 13.00 | Alexander Mikhailov (Leeds) | Lax-Darboux structures associated with Kac-Moody algebras | |
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We consider Lax operators for two-dimensional Toda type systems
corresponding to classical series of Kac-Moody algebras and
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| 14.00 | Katrin Leschke (Leicester) | Darboux transformations for conformal surfaces | |
| The classical Darboux transformations is defined for a special surface class, the isothermal surfaces. To obtain a spectral curve for conformal tori and a geometric interpretation, the Darboux transform has been generalised to general conformal immersions. In this talk , I will discuss the Darboux transform of minimal surfaces. | |||
| Maths Lecture Theatre | 15:00 | Tea | |
| 15.30 | George Papamikos (Kent) | Darboux transformations and related structures: the vector sine-Gordon case | |
| We construct the Darboux transformation for the vector sine-Gordon equation. The construction is completely algebraic and utilises the reduction group, the symmetry group of the Lax structure. We then use the Darboux transformation to make connections to integrable differential-difference equations and discrete equations which are compatible around the cube. | |||
| 16.00 | Christian Korff (Glasgow) | From Quantum Bäcklund Transforms to Topological Quantum Field Theory | |
| We derive the quantum analogue of a Bäcklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schrödinger equation. After quantisation of the Ablowitz-Ladik chain we derive a set of functional relations for the quantum transform which matches the relations of a one-variable classical Bäcklund transform to all orders in ℏ. The multi-Bäcklund transforms generate the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients. http://arxiv.org/abs/1508.06595 (to appear in Journal of Physics A) | |||
Local travel information including maps may be found here. The Rutherford annex seminar room is on the top floor of the large grey temporary building next to Rutherford college. See here.
Train information may be obtained from here. The quickest train from London to Canterbury takes 58 minutes from St Pancras.