9780821829486
Applied Picard-Lefschetz Theory - V. A. Vassiliev
American Mathematical Society (2002)
In Collection
#1593

Read It:
Yes

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 complete intersections, 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 of problems 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 mathematicians and mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.

Product Details
LoC Classification QA564.V37 2002
Dewey 516.35
Format Hardcover
Cover Price 87,00 €
No. of Pages 352
Height x Width 260 x 180 mm
Personal Details
Links Amazon