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Lectures: G. Toraldo di Francia: Lezioni sulla teoria della diffrazione elettromagnetica.- C.J. Bouwkamp: Theorie des multipoles, de l'antenne et de la diffraction des ondes.- Seminars: G. Eckart: Sur le fading des ondes ultracourtes et son analyse.- G. Agostinelli: Sulla teoria delle guide d´onda.- D. Graffi: Guide d´onda con dielettrico eterogeneo.

Cosmology. --- Electromagnetic waves. --- Microwaves. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Electromagnetic waves --- Mathematics. --- Partial differential equations. --- Optical engineering. --- Partial Differential Equations. --- Microwaves, RF and Optical Engineering. --- Differential equations, partial. --- Hertzian waves --- Electric waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Partial differential equations --- Mechanical engineering

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Lectures: C.B. Allendörfer: Global differential geometry of imbedded manifolds.- Seminars: P. Libermann: Pseudo-groupes infitésimaux.

Affine differential geometry. --- Differential Geometry. --- Global differential geometry. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Global differential geometry --- Geometry, Differential --- Mathematics. --- Differential geometry. --- Differential geometry

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L. Nirenberg: On elliptic partial differential equations.- S. Agmon: The Lp approach to the Dirichlet problems.- C.B. Morrey, Jr.: Multiple integral problems in the calculus of variations and related topics.- L. Bers: Uniformizzazione e moduli.

Difference and Functional Equations. --- Difference equations. --- Functional equations. --- Inequalities (Mathematics). --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Functional equations --- Differential equations --- 517.91 Differential equations --- Equations, Functional --- Mathematics. --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.

Differential equations, Partial --- Differential equations, Nonlinear --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Differential geometry. --- Calculus of variations. --- Analysis. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Functional Analysis. --- Differential Geometry. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Differential geometry --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Global analysis (Mathematics). --- Differential equations, partial. --- Mathematical optimization. --- Global differential geometry. --- Geometry, Differential --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Nonlinear PDEs --- CIME

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Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. Alain Valette recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. Edward Frenkel describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the ramified case where a finite number of regular singular points is allowed. Masaki Kashiwara studies the relationship between the representation theory of real semisimple Lie groups and the geometry of the flag manifolds associated with the corresponding complex algebraic groups. David Vogan deals with the problem of getting unitary representations out of those arising from complex analysis, such as minimal globalizations realized on Dolbeault cohomology with compact support. Nolan Wallach illustrates how representation theory is related to quantum computing, focusing on the study of qubit entanglement.

Harmonic analysis --- Representations of groups --- Problèmes aux limites --- Représentations de groupes --- Congresses. --- Solutions numériques --- Congrès --- Operations Research --- Algebra --- Calculus --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Mathematics. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Harmonic analysis. --- Functional analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Functions of complex variables. --- Functional Analysis. --- Topological Groups, Lie Groups. --- Abstract Harmonic Analysis. --- Non-associative Rings and Algebras. --- Global Analysis and Analysis on Manifolds. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Math --- Science --- Topological Groups. --- Algebra. --- Global analysis. --- Differential equations, partial. --- Global analysis (Mathematics) --- Partial differential equations