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Introduction to classical integrable systems
1. Introduction 2. Integrable dynamical systems 3. Synopsis of integrable systems 4. Algebraic methods 5. Analytical methods 6. The closed Toda chain 7. The Calogero-Moser model 8. IsomonodromicExpand
Fock representations and BRST cohomology inSL(2) current algebra
We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex ofExpand
Conformal Field Theories of Stochastic Loewner Evolutions
Stochastic Loewner evolutions (SLEκ) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLEκ evolutionsExpand
Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics atExpand
Yang-Baxter equation in long-range interacting systems
We consider the su(p) spin chains with long-range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying theExpand
Slow Modes in Passive Advection
The anomalous scaling in the Kraichnan model of advection of the passive scalar by a random velocity field with nonsmooth spatial behavior is traced to the presence of slow resonance-type collectiveExpand
Hidden Yangians in 2D massive current algebras
We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of theExpand
2D growth processes: SLE and Loewner chains
Abstract This review provides an introduction to two dimensional growth processes. Although it covers a variety of processes such as diffusion limited aggregation, it is mostly devoted to a detailedExpand
Energy flow in non-equilibrium conformal field theory
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperaturesExpand
Exact Solution of Long-Range Interacting Spin Chains with Boundaries
We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models.Expand
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