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Physics --- Mathematical physics --- Physique mathématique --- Periodicals --- Périodiques --- Mathematical physics. --- Mathematische fysica. --- #TS:WNAT --- Mathematical Sciences --- Mathematical Physics --- General and Others --- Physique mathématique --- Périodiques --- EJPHYSI ELSEVIER-E EPUB-ALPHA-R EPUB-PER-FT --- Physical mathematics --- Mathematics

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The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.

Operator theory --- Mathematical physics. --- Perturbation (Mathematics). --- Perturbation (Quantum dynamics). --- Schrödinger operator. --- Schrodinger operator. --- Perturbation (Quantum dynamics) --- Perturbation (Mathematics) --- Mathematical physics --- Schrèodinger operator --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Mathematische fysica --- Perturbatie (Wiskunde) --- Perturbation (Dynamique quantique) --- Perturbation (Mathématiques) --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Schrödinger [Operateur de ] --- Schrödinger operator --- Schrödingeroperator --- Storing (Quantumdynamica) --- Wiskundige fysica --- Partial differential equations. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Physics --- Partial differential equations

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The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.

Category theory. Homological algebra --- Quantum groups --- Representations of groups --- Sheaf theory --- Mathematical physics --- Mathematical Theory --- Applied Physics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Bundeltheorie --- Cohomology [Sheaf ] --- Faisceaux [Théorie des ] --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Groupes des quantiques --- Mathematische fysica --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Quanta [Groupes des ] --- Quantumgroepen --- Representation des groupes --- Sheaf cohomology --- Sheaves (Algebraic topology) --- Sheaves [Theory of ] --- Théorie des faisceaux --- Vertegenwoordiging van groepen --- Wiskundige fysica --- Algebraic geometry. --- Differential geometry. --- Topology. --- Nonassociative rings. --- Rings (Algebra). --- Algebraic topology. --- Quantum physics. --- Algebraic Geometry. --- Differential Geometry. --- Non-associative Rings and Algebras. --- Algebraic Topology. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Topology --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Differential geometry --- Algebraic geometry --- Quantum groups. --- Representations of groups. --- Sheaf theory. --- Cohomology, Sheaf --- Sheaves, Theory of --- Algebraic topology --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Quantum field theory