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Author: Kai Cieliebak
Publisher: American Mathematical Soc.
ISBN: 0821885332
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').
Author: Kai Cieliebak
Publisher: American Mathematical Soc.
ISBN: 0821885332
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').
Author: Frédéric Bourgeois
Publisher: Springer Science & Business Media
ISBN: 3319020366
Category : Science
Languages : en
Pages : 538
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Book Description
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
Author: Helmut Hofer
Publisher: Springer Nature
ISBN: 3031191110
Category : Mathematics
Languages : en
Pages : 1158
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Book Description
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Author: Chris Wendl
Publisher: Cambridge University Press
ISBN: 1108497403
Category : Mathematics
Languages : en
Pages : 197
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Book Description
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Author: Antonio Alarcón
Publisher: Springer Nature
ISBN: 3030690563
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Author: Burak Ozbagci
Publisher: Springer Science & Business Media
ISBN: 366210167X
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.
Author: Tohru Eguchi
Publisher: Cambridge University Press
ISBN: 1107056411
Category : Mathematics
Languages : en
Pages : 303
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Book Description
This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute.
Author: Piotr Kielanowski
Publisher: Springer
ISBN: 3030011569
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.
Author: Casim Abbas
Publisher: Springer
ISBN: 3030118037
Category : Mathematics
Languages : en
Pages : 328
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Book Description
This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory. An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9). The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors.
Author: Kevin Davis
Publisher: Penguin
ISBN: 1594206333
Category : Law
Languages : en
Pages : 338
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Book Description
Called “the best kind of nonfiction” by Michael Connelly, this riveting new book combines true crime, brain science, and courtroom drama. In 1991, the police were called to East 72nd St. in Manhattan, where a woman's body had fallen from a twelfth-story window. The woman’s husband, Herbert Weinstein, soon confessed to having hit and strangled his wife after an argument, then dropping her body out of their apartment window to make it look like a suicide. The 65-year-old Weinstein, a quiet, unassuming retired advertising executive, had no criminal record, no history of violent behavior—not even a short temper. How, then, to explain this horrific act? Journalist Kevin Davis uses the perplexing story of the Weinstein murder to present a riveting, deeply researched exploration of the intersection of neuroscience and criminal justice. Shortly after Weinstein was arrested, an MRI revealed a cyst the size of an orange on his brain’s frontal lobe, the part of the brain that governs judgment and impulse control. Weinstein’s lawyer seized on that discovery, arguing that the cyst had impaired Weinstein’s judgment and that he should not be held criminally responsible for the murder. It was the first case in the United States in which a judge allowed a scan showing a defendant’s brain activity to be admitted as evidence to support a claim of innocence. The Weinstein case marked the dawn of a new era in America's courtrooms, raising complex and often troubling questions about how we define responsibility and free will, how we view the purpose of punishment, and how strongly we are willing to bring scientific evidence to bear on moral questions. Davis brings to light not only the intricacies of the Weinstein case but also the broader history linking brain injuries and aberrant behavior, from the bizarre stories of Phineas Gage and Charles Whitman, perpetrator of the 1966 Texas Tower massacre, to the role that brain damage may play in violence carried out by football players and troubled veterans of America’s twenty-first century wars. The Weinstein case opened the door for a novel defense that continues to transform the legal system: Criminal lawyers are increasingly turning to neuroscience and introducing the effects of brain injuries—whether caused by trauma or by tumors, cancer, or drug or alcohol abuse—and arguing that such damage should be considered in determining guilt or innocence, the death penalty or years behind bars. As he takes stock of the past, present and future of neuroscience in the courts, Davis offers a powerful account of its potential and its hazards. Thought-provoking and brilliantly crafted, The Brain Defense marries a murder mystery complete with colorful characters and courtroom drama with a sophisticated discussion of how our legal system has changed—and must continue to change—as we broaden our understanding of the human mind.
