Many vital services of mathematical physics are outlined as integrals looking on parameters. The Picard-Lefschetz thought reviews how analytic and qualitative homes of such integrals (regularity, algebraicity, ramification, singular issues, etc.) depend upon the monodromy of corresponding integration cycles. during this publication, V. A. Vassiliev provides numerous types of the Picard-Lefschetz thought, together with the classical neighborhood monodromy idea of singularities and entire intersections, Pham's generalized Picard-Lefschetz formulation, stratified Picard-Lefschetz thought, and in addition twisted models of these kind of theories with functions to integrals of multivalued varieties. the writer additionally indicates how those models of the Picard-Lefschetz concept are utilized in learning numerous difficulties coming up in lots of components of arithmetic and mathematical physics. particularly, he discusses the subsequent periods of capabilities: quantity capabilities coming up within the Archimedes-Newton challenge of integrable our bodies; Newton-Coulomb potentials; primary options of hyperbolic partial differential equations; multidimensional hypergeometric services generalizing the classical Gauss hypergeometric indispensable. The ebook is aimed at a huge viewers of graduate scholars, examine mathematicians and mathematical physicists drawn to algebraic geometry, complicated research, singularity idea, asymptotic equipment, power idea, and hyperbolic operators.

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