This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its...
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebr...
This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. The introduction by Nigel Hitchin addresses the meaning of integrability, discussing in particular how to recognize an integrable system. He then develops connections between integrable systems and algebraic geometry and introduces Riemann surfaces, sheaves, and line bundles. In the next part, Graeme Segal takes the Korteweg-de Vries and nonlinear Schrodinger equations as central examples and discusses the mathematical structures underlying the inverse scattering...
This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. The introduction b...
This book was written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces, it proceeds quickly to the central results of the field, including the theorem of Hahn-Banach. The spaces (p Lp (X, (), C(X)' and Sebolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C-algebras, and the spectral representation for bounded normal and unbounded self-adjoint operators for...
This book was written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook ...
This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses. The over 750 exercises range...
This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of ex...
This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the...
This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It cover...
This graduate level text covers the theory of stochastic integration, an important area of mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in mathematics, statistics, probability, mathematical finance, and economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownian motion, Poisson process).
This graduate level text covers the theory of stochastic integration, an important area of mathematics that has a wide range of applications, includin...
This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the...
This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It cover...
This introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style making the student an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one semester or two quarter course, and Part II, which id problem based allows the book to be used for a year long course which supports a variety of syllabuses.
This introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and proje...
Based on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and Teichmuller theory. Assuming some familiarity with Riemann surfaces and hyperbolic geometry, topics covered include the Grotzch argument, analytical properties of quasiconformal maps, the Beltrami differential equation, holomorphic motions and Teichmuller spaces. Where proofs are omitted, references to where they may be found are always given, and...
Based on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a...
This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In Mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in Physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connections, curvature, complex and Kahler structures suitable for beginning graduate students, the text...
This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In M...
