Download or read book Invariants of Virtual Lattices Over Group Rings with Applications to Galois Module Structure written by Francois Destrempes and published by Ann Arbor, Mich. : University Microfilms International. This book was released on 1990 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Report written by Cornell University. Department of Mathematics and published by . This book was released on 1988 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1991 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1991 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1990 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Download or read book Geometric Topology Localization Periodicity and Galois Symmetry written by Dennis P. Sullivan and published by Springer. This book was released on 2009-09-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Download or read book Introduction to l2 invariants written by Holger Kammeyer and published by Springer. This book was released on 2019-10-31 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the most important concepts and problems in the field of l2-invariants. After some foundational material on group von Neumann algebras, l2-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of l2-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of l2-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with l2-torsion, twisted variants and the conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.
Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
Download or read book A Theory of Generalized Donaldson Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.
Download or read book Topological Automorphic Forms written by Mark Behrens and published by American Mathematical Soc.. This book was released on 2010-02-22 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Noncommutative Geometry Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
