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A Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry, and Topology was held at Stockholm University in May 2008. The choice of subjects of the Symposium and present volume was motivated by the work and mathematical interests of Oleg Viro to whom the Symposium and this volume are dedicated. As a professor of Uppsala University, Viro has made invaluable contributions to Swedish research by complementing the country's longstanding tradition in analysis with his own renowned expertise in geometry and topology. Consolidating in a single volume a major portion of the recent, impressive encounters among the fields of analysis, geometry, and topology would be too ambitious. The collection of papers in this work still should give some sense of the development of the fields and their interactions. The topics presented by leading experts in their respective fields include: algebraic geometry, in particular, real algebraic geometry, differential geometry, symplectic and contact geometry, complex analysis, three- and four-dimensional manifolds, and invariants of links. Also included in the book is the opening speech of the Symposium by Lennart Carleson on the Unity of Mathematics. Contributors: S. Akbulut K. Baker R. Berman A. Degtyarev J.-P. Demailly T. Ekholm Y. Eliashberg M. Entov J. Etnyre D. Gay G. Henkin I. Itenberg L. Kauffman K. Kaveh M. Khanevsky V. Kharlamov A. Khovanskii C. Manolescu N. Mishachev N. Mok S. Orevkov L. Polterovich P. Py N. Reshetikhin A. Shumakovitch E. Shustin A. Stipsicz C. Stroppel B. Webster C. Woodward.

Geometry -- Congresses. --- Mathematical analysis -- Congresses. --- Topology -- Congresses. --- Topology --- Mathematical analysis --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- 517.1 Mathematical analysis --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Geometry. --- Topology. --- Global Analysis and Analysis on Manifolds. --- Analysis. --- Global analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Euclid's Elements --- Geometry, Differential

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Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincaré-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves. Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world.

Algebra --- Partial differential equations --- Mathematical analysis --- Mathematical physics --- differentiaalvergelijkingen --- algebra --- analyse (wiskunde) --- theoretische fysica