Kernel Functions Analytic Torsion And Moduli Spaces

Author : John D. Fay
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 43,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825501

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Kernel Functions, Analytic Torsion, and Moduli Spaces by John D. Fay Pdf

This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.

Author : Toshiki Mabuchi,Junjir? Noguchi,Takushiro Ochiai
Publisher : World Scientific
Page : 268 pages
File Size : 41,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9810220677

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Geometry and Analysis on Complex Manifolds by Toshiki Mabuchi,Junjir? Noguchi,Takushiro Ochiai Pdf

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Author : Toshiki Mabuchi,J Noguchi,T Ochiai
Publisher : World Scientific
Page : 261 pages
File Size : 41,6 Mb
Release : 1994-12-09
Category : Mathematics
ISBN : 9789814501224

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Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday by Toshiki Mabuchi,J Noguchi,T Ochiai Pdf

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Author : Jay Jorgenson,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 44,6 Mb
Release : 2006
Category : Geometry, Algebraic
ISBN : 9780821836989

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The Ubiquitous Heat Kernel by Jay Jorgenson,American Mathematical Society Pdf

The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

Author : Saburou Saitoh
Publisher : CRC Press
Page : 289 pages
File Size : 42,7 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000115246

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Integral Transforms, Reproducing Kernels and Their Applications by Saburou Saitoh Pdf

The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.

Author : Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Publisher : American Mathematical Society
Page : 250 pages
File Size : 43,6 Mb
Release : 2024-04-09
Category : Mathematics
ISBN : 9781470473051

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Advances in Functional Analysis and Operator Theory by Marat V. Markin,Igor V. Nikolaev,Carsten Trunk Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Author : Alexander I. Bobenko
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 43,5 Mb
Release : 2011-02-12
Category : Mathematics
ISBN : 9783642174124

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko Pdf

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Author : Björn Engquist,Wilfried Schmid
Publisher : Springer
Page : 1219 pages
File Size : 50,6 Mb
Release : 2017-04-05
Category : Mathematics
ISBN : 9783642564789

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Mathematics Unlimited - 2001 and Beyond by Björn Engquist,Wilfried Schmid Pdf

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

Author : Pierre Albin,Frédéric Rochon,David Sher
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 45,5 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470444228

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Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps by Pierre Albin,Frédéric Rochon,David Sher Pdf

Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.

Author : Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos
Publisher : Birkhäuser
Page : 227 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880039

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Factorization and Integrable Systems by Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos Pdf

This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Author : Oscar Zariski
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 49,7 Mb
Release : 1951
Category : Algebraic functions
ISBN : 9780821812051

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Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields by Oscar Zariski Pdf

Author : Stephen Semmes
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 49,8 Mb
Release : 1992
Category : Conformal mapping
ISBN : 9780821825327

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A Generalization of Riemann Mappings and Geometric Structures on a Space of Domains in C$^n$ by Stephen Semmes Pdf

Similar in philosophy to the study of moduli spaces in algebraic geometry, the central theme of this book is that spaces of (pseudoconvex) domains should admit geometrical structures that reflect the complex geometry of the underlying domains in a natural way. With its unusual geometric perspective of some topics in several complex variables, this book appeals to those who view much of mathematics in broadly geometrical terms.

Author : Mark Levi
Publisher : American Mathematical Soc.
Page : 147 pages
File Size : 50,5 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821822449

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Qualitative Analysis of the Periodically Forced Relaxation Oscillations by Mark Levi Pdf

Author : Ralph Howard
Publisher : American Mathematical Soc.
Page : 69 pages
File Size : 51,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825693

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The Kinematic Formula in Riemannian Homogeneous Spaces by Ralph Howard Pdf

This book shows that much of classical integral geometry can be derived from the coarea formula by some elementary techniques. Howard generalizes much of classical integral geometry from spaces of constant sectional curvature to arbitrary Riemannian homogeneous spaces. To do so, he provides a general definition of an ``integral invariant'' of a submanifold of the space that is sufficiently general enough to cover most cases that arise in integral geometry. Working in this generality makes it clear that the type of integral geometric formulas that hold in a space does not depend on the full group of isometries, but only on the isotropy subgroup. As a special case, integral geometric formulas that hold in Euclidean space also hold in all the simply connected spaces of constant curvature. Detailed proofs of the results and many examples are included. Requiring background of a one-term course in Riemannian geometry, this book may be used as a textbook in graduate courses on differential and integral geometry.

Author : Arthur Erdélyi,Charles Andrew Swanson
Publisher : American Mathematical Soc.
Page : 50 pages
File Size : 40,5 Mb
Release : 1957
Category : Mathematics
ISBN : 9780821812259

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Asymptotic Forms of Whittaker's Confluent Hypergeometric Functions by Arthur Erdélyi,Charles Andrew Swanson Pdf