This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. A striking demonstration of the potential of these techniques is provided by Kont- vich's famous formula, which solves a long-standing question: How many plane rational curves of degree d pass through 3d -- 1 given points in general position? The formula expresses the number of curves for a given degree in terms of the numbers for lower degrees. A single initial datum is required for the recursion, namely, the case d = I, which simply amounts...
This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology...
This volume of invited articles by several outstanding mathematicians in algebra, algebraic geometry, and number theory is dedicated to Vladimir Drinfeld on the occasion of his 50th birthday. These surveys and original research articles broadly reflect the range of Drinfeld's work in these areas, especially his profound contributions to the Langlands program and mathematical physics. The contributors include: V.V. Fock, E. Frenkel, D. Gaitsgory, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu. Manin, and V. Schechtmann.
This volume of invited articles by several outstanding mathematicians in algebra, algebraic geometry, and number theory is dedicated to Vladimir Drinf...
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms."
The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is in...
This book presents a link between modern analysis and topology. Based upon classical Morse theory it develops the finite dimensional analogue of Floer homology which, in the recent years, has come to play a significant role in geometry. Morse homology naturally arises from the gradient dynamical system associated with a Morse function. The underlying chain complex, already considered by Thom, Smale, Milnor and Witten, analogously forms the basic ingredient of Floer's homology theory. This concept of relative Morse theory in combination with Conley's continuation principle lends itself to...
This book presents a link between modern analysis and topology. Based upon classical Morse theory it develops the finite dimensional analogue of Fl...
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C....
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techn...
Andreas Floer's visions and contributions have significantly influenced the developments of mathematics. This work presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues.
Andreas Floer's visions and contributions have significantly influenced the developments of mathematics. This work presents a collection of invited co...
The first European Congress of Mathematics was held in Paris from July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne universities. It was hoped that the Congress would constitute a symbol of the development of the community of European nations. More than 1,300 persons attended the Congress. The purpose of the Congress was twofold. On the one hand, there was a scientific facet which consisted of forty-nine invited mathematical lectures that were intended to establish the state of the art in the various branches of pure and applied mathematics. This scientific facet also included...
The first European Congress of Mathematics was held in Paris from July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne universities. It was ...
Reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions of functional analysis. This work covers topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces and partial differential operators.
Reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions of functional analysis. This work...
Award-winning monograph of the Ferran Sunyer i Balagure Prize 1996.
This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book. One of the most attractive features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point the latest discoveries as are...
Award-winning monograph of the Ferran Sunyer i Balagure Prize 1996.
This book systematically develops some methods for proving the non-vanishing ...
