By V. A. Vassiliev

Many vital services of mathematical physics are outlined as integrals counting on parameters. The Picard-Lefschetz concept reports how analytic and qualitative houses of such integrals (regularity, algebraicity, ramification, singular issues, etc.) rely on the monodromy of corresponding integration cycles. during this ebook, V. A. Vassiliev offers a number of models of the Picard-Lefschetz thought, together with the classical neighborhood monodromy thought of singularities and whole intersections, Pham's generalized Picard-Lefschetz formulation, stratified Picard-Lefschetz conception, and likewise twisted models of these kinds of theories with functions to integrals of multivalued kinds. the writer additionally exhibits how those models of the Picard-Lefschetz conception are utilized in learning various difficulties bobbing up in lots of components of arithmetic and mathematical physics. particularly, he discusses the subsequent periods of features: quantity capabilities bobbing up within the Archimedes-Newton challenge of integrable our bodies; Newton-Coulomb potentials; primary suggestions of hyperbolic partial differential equations; multidimensional hypergeometric capabilities generalizing the classical Gauss hypergeometric imperative. The ebook is aimed at a wide viewers of graduate scholars, study mathematicians and mathematical physicists attracted to algebraic geometry, advanced research, singularity conception, asymptotic equipment, strength idea, and hyperbolic operators.