The book is divided on the studied aspects in integral geometry and that are of interest in field theory, at least, to the solution or obtaining of integrals to the field equations corresponding to the moduli stacks planted. In the chapters 1, 2, 3, 4, are exposed the generalizations of the Penrose transforms with a good D-modules theory in the derived categories context and their deformations. In the chapters 5, and 6, are exposed and discussed the different classification problems and their implications in the differential operators to the field equations. Finally, in the chapters 7, and 8 are exposed the aspects of the geometrical ramification of field ramification going behold the holomorphicity. In the end of the book are included several research exercises that can be discussed and exposed inside postgraduate courses in derived geometry or related as derived categories or categories on commutative and non-commutative rings.

This book is a tribute to a universal mathematician, whose contributions to pure and applied mathematics in various fields, such as algebraic geometry, mathematical physics, infinite Lie theory, astrophysics, theoretical physics, nanotechnology and electronics, are relevant for the creation of future technologies and have facilitated a greater understanding of the universe. The book contains various anecdotes of the academic experiences of Dr Francisco Bulnes, and analyses of some of the contributions he made to his fields of study. The book will be of great interest to PhD students, providing them with motivation and inspiration for their own research projects, as well as other researchers.

The complex analysis, also known as theory of analytic functions or complex variable function theory, is the part of mathematical analysis that investigates the functions of complex numbers, their analyticity, holomorphicity, and integration of these functions on complex domains that can be complex manifolds or submanifolds. Also the extensions of these domains to the complex projective spaces and complex topological groups are study themes. The analytic continuing of complex domains where complex series representations are used and the exploring of singularities whose integration invariants obtain values as zeros of certain polynomials of the complex rings of certain vector bundles are important in the exploring of new function classes in the meromorphic context and also arithmetic context. Also important are established correspondences with complex vector spaces, or even in their real parts, using several techniques of complex geometrical analysis, Nevanlinna methods, and other techniques as the modular forms. All this is just some examples of great abundance of the problems in mathematics research that require the complex analysis application. This book covers some interesting and original research of certain topics of complex analysis. Also included are some applications for inverse and ill posed problems developed in engineering and applied research.

A numerical simulation is a computing calculation following a program that develops a mathematical model for a physical, social, economic, or biological system. Numerical simulations are required for analyzing and studying the behavior of systems whose mathematical models are very complex, as in the case of nonlinear systems. Capturing the resulting uncertainty of models based on uncertain parameters and constraints in confidence intervals (1-D), or more generally (>1-D) confidence regions, is very common for expressing to which degree the computed result is believed to be consistent with possible values of the targeted observable. This book examines the different methods used in numerical simulations, including adaptive and stochastic methods as well as finite element analysis research. This work is accompanied by studies of confidence regions, often utilized to express the credibility of such calculations and simulations.

The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).

The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.

This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.

At what point does theory depart the realm of testable hypothesis and come to resemble something like aesthetic speculation, or even theology? The legendary physicist Wolfgang Pauli had a phrase for such ideas: He would describe them as "not even wrong," meaning that they were so incomplete that they could not even be used to make predictions to compare with observations to see whether they were wrong or not. In Peter Woit's view, superstring theory is just such an idea. In Not Even Wrong , he shows that what many physicists call superstring "theory" is not a theory at all. It makes no predictions, even wrong ones, and this very lack of falsifiability is what has allowed the subject to survive and flourish. Not Even Wrong explains why the mathematical conditions for progress in physics are entirely absent from superstring theory today and shows that judgments about scientific statements, which should be based on the logical consistency of argument and experimental evidence, are instead based on the eminence of those claiming to know the truth. In the face of many books from enthusiasts for string theory, this book presents the other side of the story.

Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.