2015; approx. 340 pp; softcover
ISBN-13: 978-1-4704-2056-7
Expected publication date is September 4, 2015.
The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture.
The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.
Undergraduate and graduate students and research mathematicians interested in the history of mathematics and complex analysis.
L. Bers, R. Shapiro, and V. Bers -- Pages from a Memoir
L. Nirenberg -- Lipman Bers and partial differential equations
W. Abikoff and R. J. Sibner -- Bers--From graduate student to quasiconformal mapper
S. A. Wolpert -- Measurable Riemann mappings
A. Marden -- The Ahlfors-Bers creation of the modern theory of Kleinian groups--A small acorn grows to a mighty oak
I. Kra and B. Maskit -- The Bers embedding and (some of) its ramifications
F. P. Gardiner and L. Keen -- Lipman Bers, a retrospective
G. Riera and R. E. Rodriguez -- The Weil-Petersson geometry of a family of Riemann surfaces
H. Masur -- Legacy of work of Bers on the mapping class group
A. Basmajian and P. Susskind -- Bers' pants decomposition theorem
I. Kra -- Dennis Sullivan and Jeremy Kahn reminiscences
Y. Minsky -- Bers embeddings, skinning maps and hyperbolic geometry
N. A'Campo, L. Ji, and A. Papadopoulos -- On the early history of moduli and Teichmuller spaces
L. Bers -- Correction to "Spaces of Riemann surfaces as bounded domains"
L. Bers -- The migration of European mathematicians to America
I. Kra and H. Bass -- Lipman Bers May 22, 1914-October 29, 1993
C. S. Morawetz, C. Corillon, I. Kra, T. Weinstein, and J. Gilman -- Remembering Lipman Bers
L. Keen, T. K. Milnor, L. Sibner, I. Kra, J. Gilman, and J. Dodziuk -- Lipman Bers, a mathematical mentor
L. Keen, I. Kra, and R. E. Rodriguez -- Doctoral students of Lipman Bers
L. Keen, I. Kra, and R. E. Rodriguez -- Publications of Lipman Bers
Documents Mathematiques,Number: 13
2015; 448 pp; softcover
ISBN-13: 978-2-85629-802-2
This volume and its companion volume (see SMFDM/14) reproduce, with notes and comments, the correspondence between Jean-Pierre Serre and John Tate from 1956 to 2000. They also contain a selection of their email correspondence after 2000.
The texts are reproduced in their original language: in English or in French. Most of them are from 1956-1976. They treat questions such as the write-up of Bourbaki's Elements, Galois cohomology, rigid geometry, Tate's conjectures on algebraic cycles, formal and p-divisible groups, complex multiplication, and modular forms: congruence properties, weight 1 forms, and Galois representations.
These volumes should be useful to people interested in number theory or the history of mathematics.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Anyone interested in number theory or the history of mathematics.
Documents Mathematiques, Number: 14
2015; 521 pp; softcover
ISBN-13: 978-2-85629-803-9
Expected publication date is July 3, 2015.
This volume and its companion volume (see SMFDM/13) reproduce, with notes and comments, the correspondence between Jean-Pierre Serre and John Tate from 1956 to 2000. They also contain a selection of their email correspondence after 2000.
The texts are reproduced in their original language: in English or in French. Most of them are from 1956-1976. They treat questions such as the write-up of Bourbaki's Elements, Galois cohomology, rigid geometry, Tate's conjectures on algebraic cycles, formal and p-divisible groups, complex multiplication, and modular forms: congruence properties, weight 1 forms, and Galois representations.
These volumes should be useful to people interested in number theory or the history of mathematics.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Anyone interested in number theory or the history of mathematics.
Part of London Mathematical Society Lecture Note Series
Publication planned for: September 2015
format: Paperback
Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix, and distance matrix. The book begins with a brief survey of the main results and selected applications to related topics, including chemistry, physics, biology, computer science, and control theory. The author then proceeds to detail proofs, discussions, comparisons, examples, and exercises. Each chapter ends with a brief survey of further results. The author also points to open problems and gives ideas for further reading.
Preface
1. Introduction
2. Spectral radius
3. Least eigenvalue
4. Second largest eigenvalue
5. Other eigenvalues of the adjacency matrix
6. Laplacian eigenvalues
7. Signless Laplacian eigenvalues
8. Inequalities for multiple eigenvalues
9. Other spectra of graphs
References
Inequalities
Subject index.
Publication planned for: November 2015
format: Hardback
isbn: 9781107068520
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang?Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behavior of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.
Preface
Part I. Instantons:
1. Instantons in quantum mechanics
2. Unstable vacua in quantum field theory
3. Large order behavior and Borel summability
4. Non-perturbative aspects of Yang?Mills theories
5. Instantons and fermions
Part II. Large N:
6. Sigma models at large N
7. The 1=N expansion in QCD
8. Matrix models and matrix quantum mechanics at large N
9. Large N QCD in two dimensions
10. Instantons at large N
Appendix A. Harmonic analysis on S3
Appendix B. Heat kernel and zeta functions
Appendix C. Effective action for large N sigma models
References
Author index
Subject index.
Publication planned for: December 2015
format: Paperback
isbn: 9781107499430
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis.
1. Thoughts about numbers
2. What are prime numbers?
3. 'Named' prime numbers
4. Sieves
5. Questions about primes
6. Further questions about primes
7. How many primes are there?
8. Prime numbers viewed from a distance
9. Pure and applied mathematics
10. A probabilistic 'first' guess
11. What is a 'good approximation'?
12. Square root error and random walks
13. What is Riemann's hypothesis?
14. The mystery moves to the error term
15. Cesaro smoothing
16. A view of Li(X) ? ƒÎ(X)
17. The prime number theorem
18. The staircase of primes
19. Tinkering with the staircase of primes
20. Computer music files and prime numbers
21. The word 'spectrum'
22. Spectra and trigonometric sums
23. The spectrum and the staircase of primes
24. To our readers of part I
25. Slopes and graphs that have no slopes
26. Distributions
27. Fourier transforms: second visit
28. Fourier transform of delta
29. Trigonometric series
30. A sneak preview
31. On losing no information
32. Going from the primes to the Riemann spectrum
33. How many Įi's are there?
34. Further questions about the Riemann spectrum
35. Going from the Riemann spectrum to the primes
36. Building ƒÎ(X) knowing the spectrum
37. As Riemann envisioned it
38. Companions to the zeta function.