Lorentz Center - Integrable Systems in Quantum Theory from 8 Dec 2008 through 9 Dec 2008
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    Integrable Systems in Quantum Theory
    from 8 Dec 2008 through 9 Dec 2008







Speaker: Gleb Arutyunov


Title: Towards the solution of the AdS/CFT spectral problem

Abstract: I will discuss the recent progress towards finding the exact spectrum of the sigma model describing strings in the AdS_5 x S5 space-time.






Speaker: Harry Braden


Title: Cyclic Monopoles, Toda and Ramanujan

Abstract: Some years ago in the context of Seiberg-Witten theory Sutcliffe gave an ansatz for cyclic su(2) monopoles in terms of Toda theory. Here I will strengthen this connection and provide several new results arising from the relations between the spectral curves of these systems (and their covers) and the appropriate flows on their Jacobians. Some number theoretic problems are encountered in this work: a transcendental constraint on one family of curves is equivalent to a problem solved by Ramanujan.






Speaker: Ed Corrigan


Title: Some aspects of defects in integrable field theory

Abstract: The purpose of the talk is to discuss recent work concerning the possibility of allowing defects of 'shock' type in integrable field theory without destroying the feature of integrability. There are a number of examples though the talk will concentrate on and develop the classical and quantum features of just one of them (the sine-Gordon model).






Speaker: Andrey Marshakov


Title: First order string theory and the Kodaira-Spencer equations


Abstract: We consider the first-order bosonic string theory, perturbed by the primary operator, corresponding to the deformation of complex structure in target-space. We compute the effective action in this theory and find that its consistency with the world-sheet conformal invariance requires the Kodaira-Spenser equations to be satisfied by the target-space Beltrami differentials.

The same conclusion follows from studying directly the correlation functions in first-order conformal field theory. We discuss their and relation with the polyvertex structures in BRST approach, to be generally defined in terms of integrals over the moduli spaces of the world-sheet complex structures.






Speaker: Andrei Pogrebkov


Title: Commutator identities on associative algebras and integrability of nonlinear partial and difference equations

Abstract: It is shown that commutator identities on associative algebras generate

operator solutions of linearized versions of the integrable equations. A

dressing procedure in a special class of integral operators is introduced,

that enables to derive both nonlinear integrable equation itself and its

Lax pair from such commutator identity. As a specific example Hirota

bilinear difference equation and associated algebraic identity are







Speaker: Vladimir Rubtsov


Title: Manin matrices and Elliptic Gaudin revisited

Abstract: We construct a quadratic elliptic dynamical RLL algebra with Felder $R-$ elliptic matrix and show that $L$ is a Manin matrix. Then we obtain a quasi-commutative family from minors of $L$ and construct a quantum spectral curve for the quantum elliptic $gl_n$ Gaudin model. We revise the Separation of Variables in the case of the $gl_2$ model.






Speaker: Pol Vanhaecke


Title: Real and algebraic integrability

Abstract: After a short introduction to real integrable systems, I will discuss complex integrable systems, in particular the notion of algebraic integrability. As I will explain, the theory of Abelian varieties leads to a rigorous proof of the Kowalevski criterion.