David Borthwick – författare

Walking, Landscape and Environment explores walking as a method of research and practice in the humanities and creative arts, emerging from a recent surge of growth in urban and rural walking. This edited collection of essays from leading figures in the field presents an enquiry into, and a critique of, the methods and results of cutting-edge ‘walking research’. Walking negotiates the intersections between the human self, place and space, offering a cross-disciplinary collaborative method of research which can be utilised in areas such as ecocriticism, landscape architecture, literature, cultural geography and the visual arts. Bringing together a multitude of perspectives from different disciplines, on topics including health and wellbeing, disability studies, social justice, ecology and gender, this book provides a unique appraisal of the humanist perspective on landscape. In doing so, it challenges Romantic approaches to walking, applying new ideas in contemporary critical thought and alternative perspectives on embodiment and trans-corporeality.

Walking, Landscape and Environment explores walking as a method of research and practice in the humanities and creative arts, emerging from a recent surge of growth in urban and rural walking. This edited collection of essays from leading figures in the field presents an enquiry into, and a critique of, the methods and results of cutting-edge ‘walking research’. Walking negotiates the intersections between the human self, place and space, offering a cross-disciplinary collaborative method of research which can be utilised in areas such as ecocriticism, landscape architecture, literature, cultural geography and the visual arts. Bringing together a multitude of perspectives from different disciplines, on topics including health and wellbeing, disability studies, social justice, ecology and gender, this book provides a unique appraisal of the humanist perspective on landscape. In doing so, it challenges Romantic approaches to walking, applying new ideas in contemporary critical thought and alternative perspectives on embodiment and trans-corporeality.

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature.

Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.

This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum.  All of the material from the first edition is included and updated, and new sections have been added.

Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function.  The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds.  A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution.

The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory.  This book will serve as a valuable resource for graduate students and researchers from these and other related fields. 

Review of the first edition:

"The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)