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Hilbert Schemes of Points and Infinite Dimensional Lie Algebras

2018-02-26 Mathematics
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Release : 2018-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 888/5 ( reviews)

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Book Synopsis Hilbert Schemes of Points and Infinite Dimensional Lie Algebras by : Zhenbo Qin

Download or read book Hilbert Schemes of Points and Infinite Dimensional Lie Algebras written by Zhenbo Qin. This book was released on 2018-02-26. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.

Lectures on Hilbert Schemes of Points on Surfaces

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 569/5 ( reviews)

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Book Synopsis Lectures on Hilbert Schemes of Points on Surfaces by : Hiraku Nakajima

Download or read book Lectures on Hilbert Schemes of Points on Surfaces written by Hiraku Nakajima. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

Infinite-Dimensional Aspects of Representation Theory and Applications

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 01X/5 ( reviews)

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Book Synopsis Infinite-Dimensional Aspects of Representation Theory and Applications by : Stephen Berman

Download or read book Infinite-Dimensional Aspects of Representation Theory and Applications written by Stephen Berman. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 162/5 ( reviews)

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Book Synopsis Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by : Stephen Berman

Download or read book Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory written by Stephen Berman. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.

Analytic Number Theory, Approximation Theory, and Special Functions

2014-07-08 Mathematics
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Release : 2014-07-08
Genre : Mathematics
Kind : eBook
Book Rating : 58X/5 ( reviews)

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Book Synopsis Analytic Number Theory, Approximation Theory, and Special Functions by : Gradimir V. Milovanović

Download or read book Analytic Number Theory, Approximation Theory, and Special Functions written by Gradimir V. Milovanović. This book was released on 2014-07-08. Available in PDF, EPUB and Kindle. Book excerpt: This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

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