Topological Automorphic Forms PDF Download
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Author | : Mark Behrens |
Publisher | : American Mathematical Soc. |
Total Pages | : 167 |
Release | : 2010-02-22 |
Genre | : Mathematics |
ISBN | : 082184539X |
Download Topological Automorphic Forms Book in PDF, ePub and Kindle
The authors apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type $U(1,n-1)$. These cohomology theories of topological automorphic forms ($\mathit{TAF}$) are related to Shimura varieties in the same way that $\mathit{TMF}$ is related to the moduli space of elliptic curves.
Author | : Hossein Movasati |
Publisher | : World Scientific |
Total Pages | : 323 |
Release | : 2021-10-12 |
Genre | : Mathematics |
ISBN | : 9811238693 |
Download Modular And Automorphic Forms & Beyond Book in PDF, ePub and Kindle
The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.
Author | : Peter Sarnak |
Publisher | : American Mathematical Soc. |
Total Pages | : 443 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821828738 |
Download Automorphic Forms and Applications Book in PDF, ePub and Kindle
The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field. The book starts with the lectures of Borel on the basic theory of automorphic forms, which lay the foundation for the lectures by Cogdell and Shahidi on converse theorems and the Langlands-Shahidi method, as well as those by Clozel and Li on the Ramanujan conjectures and graphs. The analytic theory of GL(2)-forms and $L$-functions are the subject of Michel's lectures, while Terras covers arithmetic quantum chaos. The volume also includes a chapter by Vogan on isolated unitary representations, which is related to the lectures by Clozel. This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory. the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author | : Werner Müller |
Publisher | : Springer |
Total Pages | : 581 |
Release | : 2016-09-20 |
Genre | : Mathematics |
ISBN | : 3319414240 |
Download Families of Automorphic Forms and the Trace Formula Book in PDF, ePub and Kindle
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Author | : Christopher L. Douglas |
Publisher | : American Mathematical Soc. |
Total Pages | : 353 |
Release | : 2014-12-04 |
Genre | : Mathematics |
ISBN | : 1470418843 |
Download Topological Modular Forms Book in PDF, ePub and Kindle
The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Author | : Sebastian Thyssen |
Publisher | : |
Total Pages | : 0 |
Release | : 2015 |
Genre | : |
ISBN | : |
Download Expansion Principles for Topological Automorphic Forms Book in PDF, ePub and Kindle
Author | : Paul Garrett |
Publisher | : Cambridge University Press |
Total Pages | : 407 |
Release | : 2018-09-20 |
Genre | : Mathematics |
ISBN | : 1108228240 |
Download Modern Analysis of Automorphic Forms By Example: Volume 1 Book in PDF, ePub and Kindle
This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.
Author | : Anton Deitmar |
Publisher | : Springer Science & Business Media |
Total Pages | : 255 |
Release | : 2012-08-29 |
Genre | : Mathematics |
ISBN | : 144714435X |
Download Automorphic Forms Book in PDF, ePub and Kindle
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Author | : Paul Garrett |
Publisher | : Cambridge University Press |
Total Pages | : 367 |
Release | : 2018-09-20 |
Genre | : Mathematics |
ISBN | : 1108473849 |
Download Modern Analysis of Automorphic Forms By Example Book in PDF, ePub and Kindle
Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Author | : Harald Grobner |
Publisher | : World Scientific |
Total Pages | : 262 |
Release | : 2023-06-09 |
Genre | : Mathematics |
ISBN | : 9811246181 |
Download Smooth-automorphic Forms And Smooth-automorphic Representations Book in PDF, ePub and Kindle
This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.