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• Preface / Keenan Crane
• Discrete Laplace operators / Max Wardetzky
• Discrete parametric surfaces / Johannes Wallner
• Discrete mappings / Yaron Lipman
• Conformal geometry of simplicial surfaces / Keenan Crane
• Optimal transport on discrete domains / Justin Solomon

Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees.--Provided by publisher

• The curve, explicit divisors, and relations
• Descent calculations
• Minimal regular model, local invariants, and domination by a product of curves
• Heights and the visible subgroup
• The L-function and the BSD conjecture
• Analysis of J[p] and NS(Xd)tor
• Index of the visible subgroup and the Tate-Shafarevich group
• Monodromy of ℓ-torsion and decomposition of the Jacobian

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\mathbb F_p(t)$, when $p$ is prime and $r\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\mathbb F_q(t^1/d)$.
(source: Nielsen Book Data)

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
(source: Nielsen Book Data)

• Preface INTRODUCTION What Is an Insect? Growth and Reproduction Breathing and Circulation Feeding Stinging Distribution and Diversity of the California Insect Fauna Topography Geographical Distribution Diversity Microhabitats Making an Insect Collection Classification Names Synopsis of Hexapods and the Orders of Insects ACCOUNTS: SYSTEMATIC TREATMENT Coneheads (Class Protura) Two-pronged Bristletails (Class Diplura) Springtails (Class Collembola) Insects (Class Insecta)
• Acknowledgments Glossary Bibliography Online Resources Photo Credits Index About the Authors.
• (source: Nielsen Book Data)

Beautifully illustrated and approachable, this is the only California-specific, statewide book devoted to all groups of insects. Completely revised for the first time in over 40 years, Field Guide to California Insects now includes over 600 insect species, each beautifully illustrated with color photographs. Engaging accounts focus on distinguishing features, remarkable aspects of biology, and geographical distribution in the state. An accessible and compact introduction to identifying, understanding, and appreciating these often unfamiliar and fascinating creatures, this guide covers insects that readers are likely to encounter in homes and natural areas, cities and suburbs, rural lands and wilderness. It also addresses exotic and invasive species and their impact on native plants and animals. Field Guide to California Insects remains the definitive portable reference and a captivating read for beginners as well as avid naturalists. .
(source: Nielsen Book Data)

• The group theoretical formalism
• The Tannakian formalism
• The vectorial Tits building F^Γ(G)
• Affine F(G)-buildings
• Bruhat-Tits buildings.

The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.
(source: Nielsen Book Data)

• 1 Hunting on a no-good shore
• 2 Three letters will do
• 3 Tiny sparks
• 4 The undertone
• 5 The treasure map
• 6 The treasure house
• 7 Perfectly suited
• 8 The white bear bird
• 9 Beringia
• 10 A portion of their secrets
• 11 Now south
• 12 A flick of the dragon's tail
• 13 Lost flocks
• 14 A spoonful of hope
• 15 Navigating the possible
• 16 In harmony with the sun Author's note Notes Index.
• (source: Nielsen Book Data)

As the sun lowered and turned Gulf St Vincent fiery, they each called a high-pitched 'peeooowiii!', flashed their black wing-pits, spread their tail skirts and took flight. Andrew Darby follows the odysseys of two Grey Plovers, little-known migratory shorebirds, as they take previously uncharted ultramarathon flights from the southern coast of Australia to Arctic breeding grounds. On these extraordinary flights they chance predators, typhoon weather and exhaustion before they can breed, and maybe return to familiar southern feeding grounds. But the greatest threat to these, and other long-distance migrants on the flyway, is China's dragon economy, engulfing their vital Yellow Sea staging spots. The author meets the dedicated people working to save these intrepid birds, from Russia to Alaska, and the rim of the Arctic Sea to the coasts of the Southern Ocean. Out of their hard-won science he finds hope for the birds - a bright light for our times. But his journey to understand this work and these birds almost ends when he is suddenly diagnosed with an incurable cancer. Then he finds science coming to his rescue too.
(source: Nielsen Book Data)

The essential primer for physics students who want to build their physical intuition Presented in A. Zee's incomparably engaging style, this book introduces physics students to the practice of using physical reasoning and judicious guesses to get at the crux of a problem. An essential primer for advanced undergraduates and beyond, Fly by Night Physics reveals the simple and effective techniques that researchers use to think through a problem to its solution-or failing that, to smartly guess the answer-before starting any calculations. In typical physics classrooms, students seek to master an enormous toolbox of mathematical methods, which are necessary to do the precise calculations used in physics. Consequently, students often develop the unfortunate impression that physics consists of well-defined problems that can be solved with tightly reasoned and logical steps. Idealized textbook exercises and homework problems reinforce this erroneous impression. As a result, even the best students can find themselves completely unprepared for the challenges of doing actual research. In reality, physics is replete with back of the envelope estimates, order of magnitude guesses, and fly by night leaps of logic. Including exciting problems related to cutting-edge topics in physics, from Hawking radiation to gravity waves, this indispensable book will help students more deeply understand the equations they have learned and develop the confidence to start flying by night to arrive at the answers they seek. For instructors, a solutions manual is available upon request.
(source: Nielsen Book Data)

• Contents
• INTRODUCTION: The Philosopher's Stone
• KEYS AND MEASURES 00.01 The Cenozoic 00.02 The Acre and the Foot 00.03 The Taxonomic Classifications of Life 00.04 Map Icons
• 01. THE FIELD ATLAS: Maps and meaning across California's forests
• 02. THE ANCIENT FORESTS: California's Holocene crescendo
• 03. EARTH, WATER, AIR, and FIRE: California's defining forces
• 04. THE LIVING BODY: How forests thrive across California
• 05. STAND, GROVE, WOODLAND and FOREST: Vegetation alliances within arboreal California 06.01 ARBOREAL HABITATS OF CALIFORNIA: Distribution and conditions of wildlife systems
• 07. EXEMPLARY IN CHARACTER: Accessibility and impact
• 08. THE GIVING FORESTS: Beyond Value and Utility
• 09. THE FUTURE FORESTS: California's next one hundred years and beyond.
• (source: Nielsen Book Data)

The first book of a major new trilogy from artist-naturalist Obi Kaufmann From the author of The California Field Atlas (#1 San Francisco Chronicle Best Seller) comes a major work that not only guides readers through the Golden State's forested lands, but also presents a profoundly original vision of nature in the twenty-first century. The Forests of California features an abundance of Obi Kaufmann's signature watercolor maps and trail paintings, weaving them into an expansive and accessible exploration of the biodiversity that defines California in the global imagination. Expanding on the style of the Field Atlas, Kaufmann tells an epic story that spans millions of years, nearly one hundred species of trees, and an astonishing richness of ecosystems. The Forests of California is the first volume in a planned trilogy of field atlases, with The Coasts of California and The Deserts of California to follow, and Kaufmann seeks to create nothing less than a new understanding of the more-than-human world. The lessons in this book extend well beyond California's borders. If Peter Wohlleben's The Hidden Life of Trees and Richard Powers's The Overstory opened readers' eyes to the awesome power of arboreal life, The Forests of California gives readers a unique and unprecedented immersion in that power.
(source: Nielsen Book Data)

• Introduction--
• 1. Basics of stable homotopy theory--
• 2. Sequential spectra and the stable homotopy category--
• 3. The suspension and loop functors--
• 4. Triangulated categories--
• 5. Modern categories of spectra--
• 6. Monoidal structures--
• 7. Left Bousfield localisation-- Appendix. Model categories-- References-- Index.
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The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
(source: Nielsen Book Data)

• Background and notation--
• 1. Linear restriction theory--
• 2. Wave packets--
• 3. Bilinear restriction theory--
• 4. Parabolic rescaling and a bilinear-to-linear reduction--
• 5. Kakeya and square function estimates--
• 6. Multilinear Kakeya and restriction inequalities--
• 7. The Bourgain-Guth method--
• 8. The polynomial method--
• 9. An introduction to decoupling--
• 10. Decoupling for the elliptic paraboloid--
• 11. Decoupling for the moment curve--
• 12. Decouplings for other manifolds--
• 13. Applications of decoupling-- References-- Index.
• (source: Nielsen Book Data)

The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain-Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.
(source: Nielsen Book Data)

Birds' eggs are true wonders of the natural world: they are strong enough to protect the embryo as it grows and to withstand incubation by the parent, yet sufficiently fragile to allow the chick to hatch. Little wonder that the enormous diversity of avian eggs? the amazing range of shapes, sizes, colours and patterns? has long fascinated us. This stunning new book presents remarkable images of birds' eggs by the well-known landscape photographer Colin Prior side by side with his dramatic photographs of the birds' natural habitats. At a time when many human influences are having an adverse impact on the environment, these habitats are equally fragile and vulnerable to change. Loss of habitat is, in turn, a major factor in the decline of wild bird populations. The featured eggs were collected legally during the late 19th and early 20th centuries and now belong to the National Museum of Scotland in Edinburgh, which holds one of the world's largest collections of birds' eggs. Each photograph is a composite of between 40 and 80 separate exposures that were blended into a single image using specialist software. The result is an almost three-dimensional rendition of the egg, pin-sharp from the front to the back. The caption beneath each egg details the common and scientific name of the bird, the date the egg was collected, the size of the clutch, and the egg's dimensions. Each egg is shown in a diptych with a photograph of the bird's habitat, painstakingly captured at a time of year when the dominant colours of the landscape most closely resemble those of the egg.

• Introduction-- Part I. Category Theory:
• 1. Basic notions in category theory--
• 2. Natural transformations and the Yoneda lemma--
• 3. Colimits and limits--
• 4. Kan extensions--
• 5. Comma categories and the Grothendieck construction--
• 6. Monads and comonads--
• 7. Abelian categories--
• 8. Symmetric monoidal categories--
• 9. Enriched categories-- Part II. From Categories to Homotopy Theory:
• 10. Simplicial objects--
• 11. The nerve and the classifying space of a small category--
• 12. A brief introduction to operads--
• 13. Classifying spaces of symmetric monoidal categories--
• 14. Approaches to iterated loop spaces via diagram categories--
• 15. Functor homology--
• 16. Homology and cohomology of small categories-- References-- Index.
• (source: Nielsen Book Data)

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
(source: Nielsen Book Data)

• The basics of $\ell^p$-- Frames The geometry of $\ell^p$-- Weak parallelogram laws Hardy and Bergman spaces-- $\ell^p$ as a function space Some operators on $\ell^p_A$-- Extremal functions Zeros of $\ell^p_A$ functions The shift The backward shift Multipliers of $\ell^p_A$-- The Wiener algebra Bibliography Author index Subject index.
• (source: Nielsen Book Data)

The classical $\ell^{p}$ sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces $\ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $\ell^p$. Relations between the Banach space $\ell^p$ and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of $\ell^{p}_{A}$ and a discussion of the Wiener algebra $\ell^{1}_{A}$. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.
(source: Nielsen Book Data)

• Basics of graphs Trees and connectivity Structure and degrees Vertex coloring Planarity Hamiltonian graphs Matchings Generalized graph colorings Decompositions Appendices Nomenclature Bibliography Index.
• (source: Nielsen Book Data)

Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.
(source: Nielsen Book Data)

A scientist assesses the potential of stem cell therapies for treating such brain disorders as stroke, Alzheimer's disease, and Parkinson's disease. Stem cell therapies are the subject of enormous hype, endowed by the media with almost magical qualities and imagined by the public to bring about miracle cures. Stem cells have the potential to generate new cells of different types, and have been shown to do so in certain cases. Could stem cell transplants repair the damaged brain? In this book, neurobiologist Jack Price assesses the potential of stem cell therapies to treat such brain disorders as stroke, Alzheimer's disease, Parkinson's disease, and spinal cord injuries. Certainly brain disorders are in need of effective treatments. These disorders don't just kill, they disable, and conventional drug therapies have not had much success in treating them. Price explains that repairing the human brain is difficult, largely because of its structural, functional, and developmental complexity. He examines the self-repairing capacity of blood and gut cells-and the lack of such capacity in the brain; describes the limitations of early brain stem cell therapies for neurodegenerative disorders; and discusses current clinical trials that may lead to the first licensed stem cell therapies for stroke, Parkinson's and macular degeneration. And he describes the real promise of pluripotential stem cells, which can make all the cell types that constitute the body. New technologies, Price reports, challenge the very notion of cell transplantation, instead seeking to convince the brain itself to manufacture the new cells it needs. Could this be the true future of brain repair?
(source: Nielsen Book Data)

• Translator's Preface / Introduction /
• 1. Verticalism and Thematism /
• 2. From the Molecule to the Organism /
• 3. Internal Reproduction /
• 4. The Division and Socialisation of Development /
• 5. Signals-Stimuli /
• 6. 'Competence' /
• 7. Autonomous Procedures and Regulated Behaviour /
• 8. Open Formations and Markovian Jargon /
• 9. 'Crossword' Formations /
• 10. The 'Spectacle-Spectator' Complex /
• 11. I-Forms, II-Forms, III-Forms /
• 12. The Philosophy of Morphogenesis / Further Reading / Index.
• (source: Nielsen Book Data)

The philosophy of Raymond Ruyer was an important if subterranean influence on twentieth-century French thought, and explicitly engaged with by figures such as Maurice Merleau-Ponty, Georges Canguilhem, Gilbert Simondon, and Gilles Deleuze. The Genesis of Living Forms is Ruyer's most focussed and forceful analysis of a central but apparently paradoxical biological phenomenon that also presents serious problems for philosophy: embryogenesis. When a cat develops from the early stages of fertilization to an adult, what is it that makes it the same cat? How is it that a living being can at once be the same and constantly changing? Ruyer's answer to these questions unfolds through a detailed set of encounters with major scientific fields, from particle physics to social psychology, arguing that the paradox can only be dissolved by seeing the role that form plays in the ongoing development of living beings. In Ruyer's view, embryogenesis is a central problem not just in the life sciences; every thing must possess a relation to a form that is characteristic of it, from carbon atoms to embryos, and to embryologists themselves.
(source: Nielsen Book Data)

• Preface.- Big and nef classes, Futaki Invariant and resolutions of cubic threefolds.- Bottom of spectra and amenability of coverings.- Some remarks on the geometry of a class of locally conformally at metrics.- Analytical properties for degenerate equations.- On the existence problem of Einstein-Maxwell Kahler Metrics.- Local moduli of scalar-flat Kahler ale surfaces.- Singular Ricci flows II.- An inequality between complex Hessian measures of Hoelder continuous m-subharmonic functions and capacity.- A guided tour to normalized volume.- Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry.- Equivariant K-theory and Resolution I: Abelian actions.- Arsove-Huber's Theorem in Higher Dimensions.- From local index theory to Bergman kernel: a heat kernel approach.- Fourier-Mukai Transforms, Euler-Green Currents, and K-Stability.- The Variations of Yang-Mills Lagrangian.- Tian's properness conjectures: an introduction to Kahler geometry.- Ancient solutions in geometric flows.- The Kahler-Ricci flow on CP2.- Pluriclosed flow and the geometrization of complex surfaces.- From Optimal Transportation to Conformal Geometry.- Special Lagrangian Equation.- Positive scalar curvature on foliations: the enlargeability.- Kahler-Einstein metrics on toric manifolds and G-manifolds.- Some Questions in the Theory of Pseudoholomorphic Curves.
• (source: Nielsen Book Data)

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Slawomir Kolodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Riviere, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.
(source: Nielsen Book Data)