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Author : Andreas Juhl
Publisher : Unknown
Page : 724 pages
File Size : 55,7 Mb
Release : 2000-12-01
Category : Electronic
ISBN : 3034883412
Author : Andreas Juhl
Publisher : Birkhäuser
Page : 712 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883405
Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
Author : Alexander Fel'shtyn
Publisher : American Mathematical Soc.
Page : 165 pages
File Size : 42,9 Mb
Release : 2000
Category : Fixed point theory
ISBN : 9780821820902
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Author : David Ruelle
Publisher : American Mathematical Soc.
Page : 74 pages
File Size : 42,7 Mb
Release : 1994
Category : Mathematics
ISBN : 0821836013
With a general introduction to the subject, this title presents a detailed study of the zeta functions associated with piecewise monotone maps of the interval $ 0,1]$. In particular, it gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator.
Author : Yuri Tschinkel
Publisher : Universitätsverlag Göttingen
Page : 168 pages
File Size : 54,9 Mb
Release : 2007
Category : Algebraic varieties
ISBN : 9783938616772
Author : Erich Kähler
Publisher : Walter de Gruyter
Page : 986 pages
File Size : 41,8 Mb
Release : 2003
Category : Mathematics
ISBN : 311017118X
For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".
Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681920
* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Author : Gerard van der Geer,B.J.J Moonen,René Schoof
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 50,5 Mb
Release : 2005-09-14
Category : Mathematics
ISBN : 0817643974
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
Author : Venkatrama Lakshmibai,V. Balaji,V. B. Mehta,K. R. Nagarajan,K. Paranjape,P. Sankaran,R. Sridharan
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 50,5 Mb
Release : 2003-07-24
Category : Mathematics
ISBN : 3764304448
C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.
Author : Gregory Arone,John Hubbuck,Ran Levi,Michael Weiss
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 42,8 Mb
Release : 2003-11-27
Category : Mathematics
ISBN : 3764304006
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".
Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 46,7 Mb
Release : 2004-11-12
Category : Mathematics
ISBN : 0817643494
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
Author : Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 50,6 Mb
Release : 2007-11-07
Category : Mathematics
ISBN : 9780817643638
D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Author : Peter Bouwknegt,Siye Wu
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200673
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 46,8 Mb
Release : 2002-08-21
Category : Mathematics
ISBN : 0817642595
This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.
Author : Michèle Audin
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 40,9 Mb
Release : 2004-09-27
Category : Computers
ISBN : 3764321768
The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.