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Introduction to String Compactification
We present an elementary introduction to compactifications with unbroken supersymmetry. After explaining how this requirement leads to internal...
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Classification of All Quadratic Star Products on a Plane* **
In this paper we classify all quadratic star products on a plane by using Hochschild cohomology and Poisson cohomology.
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Universal Deformation Formulae for Three-Dimensional Solvable Lie Groups
We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of every...
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Open Problems
In the previous chapters we have discussed a subclass of Korotkin‚s hyperelliptic solutions to the Ernst equation with physically interesting...
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The Ernst Equation
Ernst's original motivation in .nding the Ernst equation [34] was to provide a simple scheme to construct the Kerr metric as a solution to the...
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Riemann–Hilbert Problem and Fay's Identity
In Chap. 2 we have shown that the Ernst equation can be treated as the integrability condition of an overdetermined linear di.erential system for...
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Analyticity Properties and Limiting Cases
In Chap. 3 we have used the linear system for the Ernst equation to construct solutions via Riemann–Hilbert techniques. This was done on the Riemann...
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Aspects of BRST Quantization
BRST-methods provide elegant and powerful tools for the construction and analysis of constrained systems, including models of particles, strings and...
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Supersymmetric Solitons and Topology
This lecture is devoted to solitons in supersymmetric theories. The emphasis is put on special features of supersymmetric solitons such as...
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Introduction and Overview
The first part of the 20th century saw the most revolutionary breakthroughs in the history of theoretical physics, the birth of general relativity...
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Three Lessons on the Painlevé Property and the Painlevé Equations
While this school focuses on discrete integrable systems we feel it necessary, if only for reasons of comparison, to go back to fundamentals and...
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Lie groups, singularities and solutions of nonlinear partial differential equations
It is shown how Lie group and Lie algebra theory can be used to solve partial differential equations. A method for calculating the symmetry group of...
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The method of Poisson pairs in the theory of nonlinear PDEs
The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear...
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Painlevé Kernels and Surface Defects at Strong Coupling
It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg–Witten curves can be systematically studied via...
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Analytical theory of the spin-orbit state of a binary asteroid deflected by a kinetic impactor
We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary...
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Some remarks on Bardeen-AdS black hole surrounded by a fluid of strings
We obtain a class of solutions that correspond to a generalization of the Bardeen black hole solution by solving the Einstein equations coupled to a...
