Author: Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 0
Book Description
Celebrating the 50th Anniversary of the Journal of Differential Geometry
Author: Selected Papers from the Journal of Differential Geometry 1967-2017
Author: Simon DonaldsonPublisher:
ISBN: 9781571463357
Category :
Languages : en
Pages : 432
Book Description
This volume presents twelve important papers on algebraic and complex geometry--papers that have played important roles in the development of these subjects. The subject matter ranges from the birational geometry of varieties, to geometric structures of moduli spaces in algebraic and complex geometry, to the geometry of compact and non-compact K�hler manifolds. Among the authors and topics are: Raoul Bott on a residue formula for holomorphic vector-fields; Armand Borel on metric properties of arithmetic quotients of symmetric spaces and an extension theorem; P. B. A. Kronheimer on Torelli-type theorem for gravitational instantons; Victor Guillemin on Kaehler structures on toric varieties; S. K. Donaldson on scalar curvature and stability of toric varieties; and Gang Liu on the volume growth of K�hler manifolds with nonnegative bisectional curvature. With a preface by Jun Li.
Index to the Journal of Differential Geometry, 1967-2007
Author: Publisher:
ISBN:
Category : Current developments in mathematics
Languages : en
Pages : 254
Book Description
Rationality of Varieties
Author: Gavril FarkasPublisher: Springer Nature
ISBN: 3030754219
Category : Mathematics
Languages : en
Pages : 433
Book Description
This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.
Probabilistic Methods in Geometry, Topology and Spectral Theory
Author: Yaiza CanzaniPublisher: American Mathematical Soc.
ISBN: 1470441454
Category : Education
Languages : en
Pages : 197
Book Description
This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22–26, 2016 and Probabilistic Methods in Topology, held from November 14–18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics. The workshop on Probabilistic Methods in Spectral Geometry and PDE brought together some of the leading researchers in quantum chaos, semi-classical theory, ergodic theory and dynamical systems, partial differential equations, probability, random matrix theory, mathematical physics, conformal field theory, and random graph theory. Its emphasis was on the use of ideas and methods from probability in different areas, such as quantum chaos (study of spectra and eigenstates of chaotic systems at high energy); geometry of random metrics and related problems in quantum gravity; solutions of partial differential equations with random initial conditions. The workshop Probabilistic Methods in Topology brought together researchers working on random simplicial complexes and geometry of spaces of triangulations (with connections to manifold learning); topological statistics, and geometric probability; theory of random groups and their properties; random knots; and other problems. This volume covers recent developments in several active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.
Inverse Problems for Fractional Partial Differential Equations
Author: Barbara KaltenbacherPublisher: American Mathematical Society
ISBN: 1470472775
Category : Mathematics
Languages : en
Pages : 522
Book Description
As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.
Polyfold and Fredholm Theory
Author: Helmut HoferPublisher: Springer Nature
ISBN: 3030780074
Category : Mathematics
Languages : en
Pages : 1001
Book Description
This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds. The theory generalizes certain aspects of nonlinear analysis and differential geometry, and combines them with a pinch of category theory to incorporate local symmetries. On the differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles which can have locally varying dimensions (finite or infinite-dimensional). These bundles come with an important class of sections, which display properties reminiscent of classical nonlinear Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis framework, a versatile transversality and perturbation theory is developed to also cover equivariant settings. The theory presented in this book was initiated by the authors between 2007-2010, motivated by nonlinear moduli problems in symplectic geometry. Such problems are usually described locally as nonlinear elliptic systems, and they have to be studied up to a notion of isomorphism. This introduces symmetries, since such a system can be isomorphic to itself in different ways. Bubbling-off phenomena are common and have to be completely understood to produce algebraic invariants. This requires a transversality theory for bubbling-off phenomena in the presence of symmetries. Very often, even in concrete applications, geometric perturbations are not general enough to achieve transversality, and abstract perturbations have to be considered. The theory is already being successfully applied to its intended applications in symplectic geometry, and should find applications to many other areas where partial differential equations, geometry and functional analysis meet. Written by its originators, Polyfold and Fredholm Theory is an authoritative and comprehensive treatise of polyfold theory. It will prove invaluable for researchers studying nonlinear elliptic problems arising in geometric contexts.
Surveys in Differential Geometry
Author: Huai-Dong CaoPublisher:
ISBN: 9781571461384
Category : Geometry, Algebraic
Languages : en
Pages : 0
Book Description
Selected Papers from the Journal of Differential Geometry 1967-2017, 5 Volume Set
Author: Simon DonaldsonPublisher:
ISBN: 9781571463395
Category :
Languages : en
Pages : 694
Book Description
These papers have been organized into five volumes by subject matter. The first volume deals with topology, the second with algebraic geometry, the third with geometric ideas, the fourth with geometric analysis, and the fifth with geometric flows. These five volumes provide a condensed version of the Journal of Differential Geometry, helping readers to understand the development of the field of geometry over the past fifty years.
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