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Many very important capabilities of mathematical physics are outlined as integrals counting on parameters. The Picard-Lefschetz thought stories how analytic and qualitative houses of such integrals (regularity, algebraicity, ramification, singular issues, etc.) rely on the monodromy of corresponding integration cycles. during this publication, V. A. Vassiliev provides a number of models of the Picard-Lefschetz conception, together with the classical neighborhood monodromy conception of singularities and whole intersections, Pham's generalized Picard-Lefschetz formulation, stratified Picard-Lefschetz conception, and in addition twisted types of these types of theories with functions to integrals of multivalued types. the writer additionally indicates how those types of the Picard-Lefschetz thought are utilized in learning various difficulties coming up in lots of parts of arithmetic and mathematical physics. specifically, he discusses the subsequent periods of services: quantity services bobbing up within the Archimedes-Newton challenge of integrable our bodies; Newton-Coulomb potentials; primary strategies of hyperbolic partial differential equations; multidimensional hypergeometric features generalizing the classical Gauss hypergeometric necessary. The ebook is aimed at a wide viewers of graduate scholars, examine mathematicians and mathematical physicists drawn to algebraic geometry, complicated research, singularity thought, asymptotic equipment, power concept, and hyperbolic operators.

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