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This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results.This volume introduces the reader to some basic mathematic...
This volume can be divided into two parts: a purely mathematical part with contributions on finance mathematics, interactions between geometry and physics and different areas of mathematics; another part on the popularization of mathematics and the situation of women in mathematics.
``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to deri...
This volume can be divided into two parts: a purely mathematical part with contributions on finance mathematics, interactions between geometry and physics and different areas of mathematics; another part on the popularization of mathematics and the situation of women in mathematics.
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Cet ouvrage est une réédition numérique d’un livre paru au XXe siècle, désormais indisponible dans son format d’origine.
Volumes 1-3 include section: Medical notes, abstracts, and reviews ; volumes 4-45 includes section titled: Abstracts of tuberculosis ; volumes 46- includes section titled: Abstracts.
Includes Abstracts section, previously issued separately.