Contemporary Mathematics, Volume: 648
2015; 289 pp; softcover
ISBN-13: 978-1-4704-2247-9
Expected publication date is October 22, 2015.
This volume contains the proceedings of the International Research Workshop on Periods and Motives--A Modern Perspective on Renormalization, held from July 2-6, 2012, at the Instituto de Ciencias Matematicas, Madrid, Spain.
Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics.
Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral.
Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged.
The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics.
Graduate students and research mathematicians interested in modern theoretical physics and algebraic geometry.
S. Bloch -- A note on twistor integrals
C. Bogner and M. Luders -- Multiple polylogarithms and linearly reducible Feynman graphs
P. Brosnan and R. Joshua -- Comparison of motivic and simplicial operations in mod-l-motivic and etale cohomology
S. Carr, H. Gangl, and L. Schneps -- On the Broadhurst-Kreimer generating series for multiple zeta values
C. Delaney and M. Marcolli -- Dyson-Schwinger equations in the theory of computation
C. Duhr -- Scattering amplitudes, Feynman integrals and multiple polylogarithms
V. Golyshev and M. Vlasenko -- Equations D3 and spectral elliptic curves
D. Kreimer -- Quantum fields, periods and algebraic geometry
E. Panzer -- Renormalization, Hopf algebras and Mellin transforms
I. Souderes -- Multiple zeta value cycles in low weight
S. Weinzierl -- Periods and Hodge structures in perturbative quantum field theory
K. Yeats -- Some combinatorial interpretations in perturbative quantum field theory
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Contemporary Mathematics, Volume: 649
2015; 244 pp; softcover
ISBN-13: 978-0-8218-9858-1
Expected publication date is October 22, 2015.
This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain.
The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory.
Graduate students and research mathematicians interested in number theory and its applications.
S. Arias-de-Reyna -- Automorphic Galois representations and the inverse Galois problem
A. C. Dominguez -- Two Mayer-Vietoris spectral sequences for D-modules
T. Crespo, A. Rio, and M. Vela -- From Galois to Hopf Galois: Theory and practice
A. Dujella and J. C. Peral -- Elliptic curves with torsion group Z/8Z or Z/2Z×Z/6Z
F. Fite -- Equidistribution, L-functions, and Sato-Tate groups
E. Gonzalez-Jimenez -- Covering techniques and rational points on some genus 5 curves
B. Le Stum and A. Quiros -- On quantum integers and rationals
G. Mantilla-Soler -- A space of weight 1 modular forms attached to totally real cubic number fields
G. Marquez-Campos and J. M. Tornero -- Characterization of gaps and elements of a numerical semigroup using Groebner bases
A. Minguez and V. Secherre -- Classification des representations modulaires de GLn(q) caracteristique non naturelle
E. Nagel -- Fractional p-adic differentiability under the Amice transform
F. P. Romo -- Reciprocity laws related to finite potent endomorphisms
D. Raboso -- When the modular world becomes non-holomorphic
Graduate Studies in Mathematics, Volume: 165
2015; 706 pp; hardcover
ISBN-13: 978-1-4704-1554-9
Expected publication date is November 29, 2015.
This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and bner bases.Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Grobner bases.
Graduate students and researchers interested in learning and teaching algebra.
Course I
Classical formulas
Classical number theory
Commutative rings
Groups
Galois theory
Appendix: Set theory
Appendix: Linear Algebra
Course II
Modules
Zorn's lemma
Advanced linear algebra
Categories of modules
Multilinear algebra
Commutative algebra II
Appendix: Categorical limits
Appendix: Topological spaces
Bibliography
Special notation
Index
AMS Chelsea Publishing, Volume: 376
2015; 575 pp; hardcover
ISBN-13: 978-1-4704-2544-9
Expected publication date is December 5, 2015.
This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book.
One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series.
The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author.
Undergraduate and graduate students interested in real analysis.
Preliminaries
Numbers
Sequences and series
Limits and continuity
Differentiation
The elementary transcendental functions
Integration
Infinite series and infinite products
Trigonometric series
Bibliography
Other works by the author
Index