Author: Claus Hertling
Publisher: Cambridge University Press
Keywords: singularities, spaces, moduli, manifolds, frobenius
Number of Pages: 250
Published: 2002-08-15
List price: $115.99
ISBN-10: 0521812968
ISBN-13: 9780521812962

For those working in singularity theory or other areas of complex geometry, this volume will open the door to the study of Frobenius manifolds. In the first part Hertling explains the theory of manifolds with a multiplication on the tangent bundle. He then presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will benefit from this careful and sound study of the fundamental structures and results in this exciting branch of mathematics.

Authors:W. K. Nicholson, M. F. Yousif,
Publisher: Cambridge University Pre
Keywords: tracts, mathematics, cambridge, rings, frobenius, quasi
Number of Pages: 326
Published: 2003-09-08
List price: $115.99
ISBN-10: 0521815932
ISBN-13: 9780521815932

This book provides an elementary, complete account of quasi-Frobenius rings at a level allowing researchers and graduate students to gain entry to the field. A ring is called quasi-Frobenius if it is "right" or "left" selfinjective, and "right" or "left" artinian (all four combinations are equivalent). The study of these rings grew out of the theory of representations of a finite group as a group of matrices over a field, and the present extent of the theory is wide-ranging.Book DescriptionA ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all fo

Author: Claude Sabbah
Publisher: Springer
Keywords: introduction, universitext, manifolds, frobenius, deformations, isomonodromic
Number of Pages: 279
Published: 2007-12-19
List price: $59.95
ISBN-10: 1848000537
ISBN-13: 9781848000537

The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of th

Author: Jorge L. Ramírez Alfonsín
Publisher: Oxford University Press, USA
Keywords: series, mathematics, applications, lecture, oxford, frobenius, problem, diophantine
Number of Pages: 260
Published: 2006-02-02
List price: $150.00
ISBN-10: 0198568207
ISBN-13: 9780198568209

During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,,an, find the largest natural number (called the Frobenius number and denoted by g(a1,,an) that is not representable as a nonnegative integer combination of a1,,an. At first glance FB may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of ma

Authors:Michel Brion, Shrawan Kumar,
Publisher: Birkhäuser Boston
Keywords: theory, progress, mathematics, representation, geometry, splitting, methods, frobenius
Number of Pages: 250
Published: 2004-12-10
List price: $99.00
ISBN-10: 0817641912
ISBN-13: 9780817641917

The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and representation theory. This work systematically develops the theory and covers all its major developments. Key topics and features: • Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings-definitions, properties and examples-to cutting edge research • Studies in detail the geometry of Schubert varieties, their syzygies, equivariant embeddings of reductive groups, Hilbert Schemes, canonical splittings, good filtrations, among other t

Authors:Nicholas M. Katz, Peter Sarnak,
Publisher: American Mathematical Society
Keywords: publications, amer, mathematical, soc, colloquium, monodromy, matrices, frobenius, eigenvalues, random
Number of Pages: 419
Published: 1998-11-24
List price: $80.00
ISBN-10: 0821810170
ISBN-13: 9780821810170

The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to inf

Author: Yuri I. Mani
Publisher: American Mathematical Society
Keywords: society, mathematical, colloquium, publications, volume, american, spaces, manifolds, quantum, cohomology, moduli, frobenius
Number of Pages: 303
Published: 1999-09-01
List price: $61.00
ISBN-10: 0821819178
ISBN-13: 9780821819173

This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author’s approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes t