Mathematics No. I Contributions to the Geometry of the Triangle
by Judson Roberts
Geometry, Dynamics and Topology of Foliations
by Bruno Scardua and Carlos Arnoldo Morales Rojas
This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in mechanics. Topics covered include Pfaffian forms, systems in n-dimensional space, and foliations and their Godbillion-Vey invariant. There is much interest in the study of geometrical objects in n-dimensional Euclidean space and this volume provides a us...
Deformations of Mathematical Structures
These Proceedings contain selected papers by the speakers invited to the Seminar on Deformations, organized in 1985/87 by Julian tawryno- wicz (t6dz), whose most fruitful parts took place in 1986 in Lublin during the 3rd Finnish-Polish Summer School in Complex Analysis [in cooperation with O. Martio (JyvliskyHl)] held simultaneously with the 9th Conference on Analytic Function in Poland [in cooperation with S. Dimiev (Sofia), P. Dolbeault (Paris), K. Spallek (Bochum), and E. Vesen- tini (Pisa)]....
Knot Invariants and Higher Representation Theory (Memoirs of the American Mathematical Society)
by Ben Webster
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ and by Mazorchuk-Stroppel and Sussan for $\mathfrak{sl}_n$. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These ar...
Zariski Geometries: Geometry from the Logician S Point of View (London Mathematical Society Lecture Note)
by Boris Zilber
These volumes contain carefully edited selections of papers that were presented at the Symposium on Trends in Approximation Theory, held in May 2000, and at the Oslo Conference on Mathematical Methods for Curves and Surfaces, held in July 2000. Both contain several invited surveys written by leading experts in the field, along with contributed research papers on the most current developments in approximation theory and in the theory and application of curves and surfaces. These books will be of...
An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics, #10)
by Meinolf Geck
An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie t...
Open Problems in Arithmetic Algebraic Geometry (Advanced Lectures in Mathematics)
This book originated in the idea that open problems act as crystallization points in mathematical research. Mathematical books usually deal with fully developed theories. But here we present work at an earlier stage-when challenging questions can give new directions to mathematical research. In mathematics, significant progress is often made by looking at the underlying structures of open problems and discovering new directions that are developed to find solutions. In that process, the search f...
Vector Bundles on Curves - New Directions (C.I.M.E. Foundation Subseries, #1649) (Lecture Notes in Mathematics, #1649)
by Shrawan Kumar, Gerard Laumon, and Ulrich Stuhler
The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of...
Integrable Systems and Foliations (Progress in Mathematics, #145)
by Claude Albert, Robert Brouzet, and Jean P. Dufour
The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino. The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.
This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete an...
Deformation Theory of Discontinuous Groups (De Gruyter Expositions in Mathematics)
by Ali Baklouti
This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and ref...
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algeb...
Non-vanishing of L-Functions and Applications (Progress in Mathematics, #157)
by Ram M. Murty and Kumar V. Murty
This monograph brings together a collection of results on the non-vanishing of L functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer...
Foundations of Algebraic Topology (Princeton Legacy Library)
by Samuel Eilenberg and Norman Steenrod
The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original...
L'Isomorphisme Entre Les Tours De Lubin-Tate ET De Drinfeld (Progress in Mathematics)
by Laurent Fargues, Alain Genestier, and Vincent Lafforgue
Ce livre contient une demonstration detaillee et complete de l'existence d'un isomorphisme equivariant entre les tours p-adiques de Lubin-Tate et de Drinfeld. Le resultat est etabli en egales et inegales caracteristiques. Il y est egalement donne comme application une demonstration du fait que les cohomologies equivariantes de ces deux tours sont isomorphes, un resultat qui a des applications a l'etude de la correspondance de Langlands locale. Au cours de la preuve des rappels et des complements...
Introduction to Hodge Theory (SMF/AMS Texts & Monographs)
Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects: $L^2$ Hodge th...