Many vital features of mathematical physics are outlined as integrals looking on parameters. The Picard-Lefschetz conception stories how analytic and qualitative houses of such integrals (regularity, algebraicity, ramification, singular issues, etc.) depend upon the monodromy of corresponding integration cycles. during this publication, V. A. Vassiliev offers numerous types of the Picard-Lefschetz idea, together with the classical neighborhood monodromy conception of singularities and entire intersections, Pham's generalized Picard-Lefschetz formulation, stratified Picard-Lefschetz idea, and in addition twisted types of a majority of these theories with purposes to integrals of multivalued types. the writer additionally exhibits how those models of the Picard-Lefschetz idea are utilized in learning various difficulties coming up in lots of components of arithmetic and mathematical physics. particularly, he discusses the subsequent periods of services: quantity capabilities bobbing up within the Archimedes-Newton challenge of integrable our bodies; Newton-Coulomb potentials; primary ideas of hyperbolic partial differential equations; multidimensional hypergeometric services generalizing the classical Gauss hypergeometric critical. The e-book is aimed at a huge viewers of graduate scholars, examine mathematicians and mathematical physicists drawn to algebraic geometry, advanced research, singularity conception, asymptotic tools, capability conception, and hyperbolic operators.
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