Part of London Mathematical Society Lecture Note Series
available from March 2016
format: Paperback
isbn: 9781107546295
In its simplest form, Hodge theory is the study of periods ? integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.
Preface Matt Kerr and Gregory Pearlstein
Introduction Matt Kerr and Gregory Pearlstein
List of conference participants
Part I. Hodge Theory at the Boundary: Part I(A). Period Domains and Their Compactifications: Classical period domains R. Laza and Z. Zhang
The singularities of the invariant metric on the Jacobi line bundle J. Burgos Gil, J. Kramer and U. Kuhn
Symmetries of graded polarized mixed Hodge structures A. Kaplan
Part I(B). Period Maps and Algebraic Geometry: Deformation theory and limiting mixed Hodge structures M. Green and P. Griffiths
Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory S. Usui
The 14th case VHS via K3 fibrations A. Clingher, C. Doran, A. Harder, A. Novoseltsev and A. Thompson
Part II. Algebraic Cycles and Normal Functions: A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces M. Asakura
A relative version of the Beilinson?Hodge conjecture R. de Jeu, J. D. Lewis and D. Patel
Normal functions and spread of zero locus M. Saito
Fields of definition of Hodge loci M. Saito and C. Schnell
Tate twists of Hodge structures arising from abelian varieties S. Abdulali
Some surfaces of general type for which Bloch's conjecture holds C. Pedrini and C. Weibel
Part III. The Arithmetic of Periods: Part III(A). Motives, Galois Representations, and Automorphic Forms: An introduction to the Langlands correspondence W. Goldring
Generalized Kuga?Satake theory and rigid local systems I ? the middle convolution S. Patrikis
On the fundamental periods of a motive H. Yoshida
Part III(B). Modular Forms and Iterated Integrals: Geometric Hodge structures with prescribed Hodge numbers D. Arapura
The Hodge?de Rham theory of modular groups R. Hain.
Part of London Mathematical Society Lecture Note Series
available from March 2016
format: Paperback
isbn: 9781316502594
The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Bockle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta value
Introduction
1. Ą-sheaves, crystals, and their trace functions
2. Functors between categories of crystals
3. The Woods Hole trace formula
4. Elementary applications
5. Crystals with coefficients
6. Cohomology of symmetric powers of curves
7. Trace formula for L-functions
8. Special values of L-functions
Appendix A. The trace formula for a transversal endomorphism.
Memoires de la Societe Mathematique de France, Number: 142
2015; 138 pp; softcover
ISBN-13: 978-2-85629-812-1
Expected publication date is October 24, 2015.
The authors show that a simple Levi compatibility condition determines stability of WKB solutions to semilinear hyperbolic initial-value problems issued from highly oscillating data. If this condition is satisfied, the solutions are defined over time intervals independent of the wavelength, and the associated WKB solutions are stable under a large class of initial perturbations. If it is not satisfied, arbitrarily small initial perturbations can destabilize the WKB solutions in small time. The authors' examples include coupled Klein-Gordon systems and systems describing Raman and Brillouin instabilities.
Graduate students and research mathematicians interested in high-frequency oscillations and hyperbolic systems.
Introduction
Assumptions and results
Main proof
Other proofs
Examples
Appendix
Bibliography
628 pages | 400 Diagrams | 312X156mm
978-0-19-945279-8 | Paperback | October 2015 (estimated)
Presents mid chapter boxed items, 'check your progress' sections, and chapter-end multiple choice questions with answers
Provides numerous solved examples and exercises grouped under different themes within every chapter
Presents truth table values for conditional statements in context with an example
Discusses an exclusive section on coding theory and digital logic
Presents related research work and application in brief at the end of every chapter connecting to the concepts discussed in that chapter
Discrete Mathematics is a textbook designed for the students of computer science engineering, information technology, and computer applications to help them develop their foundations of theoretical computer science.
With a detailed introduction to the propositional logic, set theory, and relations, the book in further chapters explores the mathematical notions of functions, integers, counting techniques, probability, discrete numeric functions and generating functions, recurrence relations, algebraic structures, poset and lattices. The discussion ends with the chapter on theory of formal and finite automata, graph theory and applications of discrete mathematics in various domains.
Adopting a solved problems approach to explaining the concepts, the book presents numerous theorems, proofs, practice exercises, and multiple choice questions.
Readership: Primary: Core for CSE, IT and MCA. Secondary: Engineering Diploma.
New in Paperback
160 pages | 246x171mm
978-0-19-875409-1 | Paperback | November 2015 (estimated)
Unique pedagogical concept makes it accessible to undergraduate level
Gives practical coverage of all topics of random walk theory used in physics and chemistry
Includes the most up-to-date results
Well illustrated, including tutorial summaries, many exercises and examples
Solutions manual available fo instructors
The name "random walk" for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of "Nature". The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier such a problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays the theory of random walks has proved useful in physics and chemistry (diffusion, reactions, mixing flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub- and super-diffusive transport processes as well. This book discusses the main variants of random walks and gives the most important mathematical tools for their theoretical description.
Undergraduate and graduate students in physics and chemistry and lecturers in the same disciplines; postgraduate students in the same disciplines and in biology; scientific workers entering a field where random walk models are used.
1: Characteristic Functions
2: Generating Functions and Applications
3: Continuous Time Random Walks
4: CTRW and Aging Phenomena
5: Master Equations
6: Fractional Diffusion and Fokker-Planck Equations for Subdiffusion
7: Levy Flights
8: Coupled CTRW and Levy Walks
9: Simple Reactions: A+B->B
10: Random Walks on Percolation Structures