Applied Picard Lefschetz Theory is popular PDF and ePub book, written by V. A. Vasilʹev in 2002, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Applied Picard Lefschetz Theory can be Read Online from any device for your convenience.
Applied Picard Lefschetz Theory Book PDF Summary
Many important functions of mathematical physics are defined as integrals depending on parameters. The Picard-Lefschetz theory studies how analytic and qualitative properties of such integrals (regularity, algebraicity, ramification, singular points, etc.) depend on the monodromy of corresponding integration cycles. In this book, V. A. Vassiliev presents several versions of the Picard-Lefschetz theory, including the classical local monodromy theory of singularities and completeintersections, Pham's generalized Picard-Lefschetz formulas, stratified Picard-Lefschetz theory, and also twisted versions of all these theories with applications to integrals of multivalued forms. The author also shows how these versions of the Picard-Lefschetz theory are used in studying a variety ofproblems arising in many areas of mathematics and mathematical physics. In particular, he discusses the following classes of functions: volume functions arising in the Archimedes-Newton problem of integrable bodies; Newton-Coulomb potentials; fundamental solutions of hyperbolic partial differential equations; multidimensional hypergeometric functions generalizing the classical Gauss hypergeometric integral. The book is geared toward a broad audience of graduate students, research mathematiciansand mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
Detail Book of Applied Picard Lefschetz Theory PDF
- Author : V. A. Vasilʹev
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821829486
- Genre : Mathematics
- Total Page : 338 pages
- Language : English
- PDF File Size : 11,5 Mb
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