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Dynamics, Geometry, Number Theory
"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--
Dynamics, Ergodic Theory and Geometry
Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.
Rigidity in Dynamics and Geometry
This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched i...
THE QUIET TIDES OF BORDEAUX
In a quiet suburb of Bordeaux, France, memories from the last century haunt the thoughts of a retired, lonely widow, night after night. Time is running out for this former schoolmistress: she opens up to a stranger, the narrator, to have her story serve as a lesson for the next generation. In the process, she is led to revisit a wartime decision, involving a forbidden romance, deeply rooted in wolf-pack psychology. In spite of her upbringing and redemption in her career, she finally comes to question her sacrifice. In the end, her ordeal will be acknowledged by a coincidence. - Maps, Drawings, Photos, Letters, Poem, Notes. (Also as paperback.)
Geometry and Physics
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
The Pyrenees
A resource book covering the finest walks, treks and climbs in the High Pyrenees for 400km between France and Spain, from the Cirque de Lescun, on the edge of the Basque country in the west, to the Carlit massif and the Cerdagne to the east of Andorra. The book is divided into five regional chapters: the Western Valleys; Cirques and Canyons; the Central Pyrenees; Enchanted Mountains; and Andorra and the Eastern High Pyrenees. Intended as a resource book for those planning a range of mountain activities in the Pyrenees, the guide describes each area valley by valley, and provides information on access and accommodation, as well as recommended maps and guidebooks. Unlike a conventional walking...
Geometry And Topology Of Submanifolds - Proceedings Of The Meeting At Luminy Marseille
Contents:Morse Theory of Minimal Two-Spheres and Curvature of Riemannian Manifolds (J D Moore)Isoparametric Systems (A West)The Gauss Map of Flat Tori in S3 (J L Weiner)On Totally Real Surfaces in Sasakian Space Forms (B Opozda)The Riemannian Geometry of Minimal Immersions of S2 into CPn (J Bolton & L M Woodward)Totally Real Submanifolds (F Urbano)Notes on Totally Umbilical Submanifolds (R Deszcz)Totally Complex Submanifolds of Quaternionic Projective Space (A Martínez)Symmetries of Compact Symmetric Spaces (B Y Chen)Nonnegatively Curved Hypersurfaces in Hyperbolic Space (S B Alexander & R J Currier)Semi-Parallel Immersions (J Deprez)Parallel Hypersurfaces (S A Robertson)Surfaces in Spheres and Submanifolds of the Nearly Kaehler 6–Sphere (F Dillen & L Vrancken)Semi-Symmetric Hypersurfaces (I van de Woestijne)Canonical Affine Connection on Complex Hypersurfaces of the Complex Affine Space (F Dillen & L Vrancken)and other papers Readership: Mathematicians.
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkähler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.
