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Author: J. William Helton
Publisher: American Mathematical Soc.
Published: 1987
Total Pages: 152
ISBN-13: 0821807188
DOWNLOAD EBOOKExpands the lectures given at a regional conference in Lincoln, Nebraska which brought together a wide variety of scientists, pure mathematicians and engineers.
Author: Susan Montgomery
Publisher: American Mathematical Soc.
Published: 1993-10-28
Total Pages: 258
ISBN-13: 0821807382
DOWNLOAD EBOOKThe last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Author: Edward G. Effros
Publisher: American Mathematical Soc.
Published: 1981
Total Pages: 90
ISBN-13: 0821816977
DOWNLOAD EBOOKDiscusses elementary algebras and $C DEGREES*$-algebras, namely those which are direct limits of complex semi simple al
Author: Henri Darmon
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 146
ISBN-13: 0821828681
DOWNLOAD EBOOKThe book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Author: Masayoshi Nagata
Publisher: American Mathematical Soc.
Published: 1978
Total Pages: 102
ISBN-13: 0821838822
DOWNLOAD EBOOKThis volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.
Author: Charles C. Conley
Publisher: American Mathematical Soc.
Published: 1978-12-31
Total Pages: 102
ISBN-13: 0821816888
DOWNLOAD EBOOKThis volume contains lectures from the Conference Board of Mathematical Sciences meeting held at the University of Colorado on May 31-June 4, 1976. The lectures consist of an expository discussion of basic results for topological flows and a somewhat more detailed discussion of isolated invariant sets and continuation. The construction of the index for isolated invariant sets is new and allows more general application than previous ones. Also, the index itself is endowed with more structure and the continuation theorem is modified to take this new structure into account. Some elementary applications are given, but the main emphasis is on the abstract theory.
Author: Tsit-Yuen Lam
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 158
ISBN-13: 0821807021
DOWNLOAD EBOOKPresents an introduction to ordered fields and reduced quadratic forms using valuation-theoretic techniques. This book describes the techniques of residue forms and the relevant Springer theory.
Author: Clifford Taubes
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 98
ISBN-13: 0821803239
DOWNLOAD EBOOKIn this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but is is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.
Author: Walter A. Strauss
Publisher: American Mathematical Soc.
Published: 1990-01-12
Total Pages: 106
ISBN-13: 0821807250
DOWNLOAD EBOOKThe theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Author: Alan Weinstein
Publisher: American Mathematical Soc.
Published: 1977
Total Pages: 58
ISBN-13: 0821816799
DOWNLOAD EBOOKFeatures notes with sections containing a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. This title also includes sections dealing with various aspects of the quantization problem, as wel as those giving a feedback of ideas from quantization theory into symplectic geometry itslef.
