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Author: Alexander Polishchuk
Publisher: Cambridge University Press
ISBN: 0521808049
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Author: Alexander Polishchuk
Publisher: Cambridge University Press
ISBN: 0521808049
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Author: L. Auslander
Publisher: Springer
ISBN: 3540374051
Category : Mathematics
Languages : en
Pages : 104
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Book Description
Author: Răzvan Gelca
Publisher: World Scientific
ISBN: 9814520594
Category : Mathematics
Languages : en
Pages : 468
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Book Description
This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology. Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern–Simons theory will find here an introduction using the simplest case, that of abelian Chern–Simons theory. Moreover, the construction of abelian Chern–Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done. Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study. Contents:PrologueA Quantum Mechanical PrototypeSurfaces and CurvesThe Theta Functions Associated to a Riemann SurfaceFrom Theta Functions to KnotsSome Results About 3- and 4-Dimensional ManifoldsThe Discrete Fourier Transform and Topological Quantum Field TheoryTheta Functions in the Quantum Group PerspectiveAn Epilogue — Abelian Chern–Simons Theory Readership: Graduate students and young researchers with an interest in complex analysis, mathematical physics, algebra geometry and low dimensional topology. Keywords:Theta Functions;ChernâSimons Theory;Knots;Skein Modules;Linking Number;Topological Quantum Field TheoryKey Features:A detailed study of the skein modules of the linking number, which provide the simplest example of a skein module (skein modules have become a major object of study in combinatorial topology)A complete discussion of the facts from low dimensional topology (Kirby's theorem, the Lickorish–Walace theorem, Wall's non-additivity of the signature) which are fundamental in Chern–Simons theoryReviews: “It looks like a really good book, presenting its many themes in a very accessible and clear fashion, replete with plenty of pictures and lots of wonderful theorems and proofs from representation theory as well as differential geometry and the kind of functional analysis needed to do quantum physics.” Mathematical Association of America
Author: L. Auslander
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Author: Richard Bellman
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Originally published: New York: Rinehart and Winston, 1961.
Author: Leon Ehrenpreis
Publisher: American Mathematical Soc.
ISBN: 0821814842
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Author: Jun-ichi Igusa
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 254
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Book Description
The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e. , after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I. A. S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W. L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C.
Author: Christina Birkenhake
Publisher: Springer Science & Business Media
ISBN: 3662063077
Category : Mathematics
Languages : en
Pages : 635
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Book Description
This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.
Author: Louis Auslander
Publisher: American Mathematical Soc.
ISBN: 0821816845
Category : Mathematics
Languages : en
Pages : 106
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Book Description
Consists of three chapters covering the following topics: foundations, bilinear forms and presentations of certain 2-step nilpotent Lie groups, discrete subgroups of the Heisenberg group, the automorphism group of the Heisenberg group, fundamental unitary representations of the Heisenberg group, and the Fourier transform and the Weil-Brezin map.
Author: Jaques Calmet
Publisher: Springer Science & Business Media
ISBN: 9783540167761
Category : Computers
Languages : en
Pages : 430
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Book Description
