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Modular forms and string duality

Modular forms and string duality

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Published by American Mathematical Society, Fields Institute for Research in Mathematical Sciences in Providence, R.I, Toronto, Canada .
Written in English

    Subjects:
  • Forms, Modular -- Congresses,
  • Duality (Mathematics) -- Congresses,
  • Mirror symmetry -- Congresses,
  • Number theory -- Congresses,
  • String theory -- Congresses,
  • Particles (Nuclear physics) -- Congresses

  • Edition Notes

    StatementNoriko Yui, Helena Verrill, Charles F. Doran, editors.
    GenreCongresses.
    SeriesFields Institute communications -- 45
    ContributionsYui, Noriko., Verrill, Helena., Doran, Charles F., 1971-
    Classifications
    LC ClassificationsQA243 .M695 2008
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL16944783M
    ISBN 109780821844847
    LC Control Number2008028173

    BPS states and bounds Heterotic/type-I duality in ten dimensions Type-IIA versus M-theory M-theory and the E8xE8 heterotic string Self-duality of the type-IIB string D-branes are the type-II R-R charged states D-brane actions Heterotic/type-II . The Banff International Research Station will host the "Modular Forms in String Theory" workshop from September 25th to September 30th, In the last two and half decades, the world has seen explosive interactions between Number Theory, Arithmetic and Algebraic Geometry, and Theoretical Physics (in particular, String Theory). To name a few.

    Abstract: At present, computer packages for working with classical modular forms are available in Magma and in Sage, both based on modular or Manin symbols. I will describe a new and extensive package available in Pari/GP based on trace formulas, including in particular modular forms of weight 1. This answer addresses one striking example for the second question: how modular forms relate to other mathematical topics. Values of zeta-functions can arise as the constant terms of nice modular forms, suitably normalized, and this lets knowledge of the higher degree Fourier coefficients impart knowledge to the user about the arithmetic nature of the constant terms that are of more direct.

    1 Introduction The study of modular forms is typically reserved for graduate students, because the amount of background needed to fully appreciate many of the constructions and methods is rather large. However, it is possible to get a rst look at modular forms without relying too heavily on the theory of complex analysis, harmonic analysis,File Size: KB. 4 D. Zagier The modular group takes its name from the fact that the points of the quotient space Γ1\H are moduli (= parameters) for the isomorphism classes of elliptic curves over C. To each point z∈ H one can associate the lattice Λ z = Z.z+ Z.1 ⊂C and the quotient space E z = C/Λ z, which is an elliptic curve, i.e., it is at the same time a complex curve and an abelian group.


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Modular forms and string duality Download PDF EPUB FB2

Get this from a library. Modular forms and string duality. [Noriko Yui; Helena Verrill; Charles F Doran;] -- "This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality.

Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem. Through its quest to unify the spectacularly successful theories of quantum mechanics and general relativity, string theory has long suggested deep connections between branches of mathematics such as topology, geometry, representation theory, and.

Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem. Through its quest to unify the spectacularly successful theories of quantum mechanics and general relativity, string theory has long suggested deep connections between branches of mathematics such as topology, geometry, representation theory, and combinatorics.

In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory.

Free Online Library: Modular forms and string duality; proceedings.(Brief article, Book review) by "SciTech Book News"; Publishing industry Library and information science Science and technology, general Books Book reviews.

Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem. Through its quest to unify the spectacularly successful theories of quantum mechanics and general relativity, string theory has long suggested deep connections between branches of mathematics such as topology, geometry, representation theory, and combinatorics.

Less. This is a book about the theory of topological modular forms. It is also a record of the e orts of a group of graduate students to learn that theory at the Talbot Workshop, and so a book born of and steeped in the Talbot vision.

In the fall ofMike Hopkins taught a course at MIT about tmf. Our gen. duality and F-Theory/Heterotic string duality have also, more recently, led to a series of mathematical conjectures, many involving elliptic curves, K3 surfaces, and modular forms.

Modular forms and quasi-modular forms play a central role in mir-ror symmetry, in particular as generating functions counting the number of curves. The ring of modular forms is a graded Lie algebra since the Lie bracket [,] = ′ − ′ of modular forms f and g of respective weights k and ℓ is a modular form of weight k + ℓ + 2.

In fact, a bracket can be defined for the n -th derivative of modular forms and such a bracket is called a Rankin–Cohen brackets. Buy Modular Forms and String Duality from Waterstones today. Click and Collect from your local Waterstones or get FREE UK delivery on orders over £ This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered \(A_\infty\)-algebras.

This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. 2, Hilbert and Siegel modular forms, trace formulas, p-adic modular forms, and modular abelian varieties, all of which are topics for additional books.

We also rarely analyze the complexity of the algorithms, but instead settle for occasional remarks about their practical efficiency. For most of this book we assume the reader has some prior File Size: 2MB. Modular forms are generalisations of functions like theta functions.

They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products.

The Fourier coefficients also arise in certain representational Cited by: Modular Forms and String Duality | Noriko Yui (Editor), Helena Verrill (Editor), Charles F. Doran (Editor) | download | B–OK.

Download books for free. Find books. This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics.

This book offers something new, which may satisfy the desire of such a by: 6. String theory is a very large area of research with many subjects beyond the scope of this thesis.

In chapter2, some fundamental concepts of string theory are introduced followed by a more detailed motivation for studying automorphic forms in string theory discussing non-perturbative contributions to four-graviton scatteringamplitudesbasedon[4 Author: Henrik P.

Gustafsson. The book"A first course in modular forms" by F. Diamond, J. Shurman is a good book to start to study classical modular forms. The advanced one "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms.

Good luck. In the past 30 years, modular and quasimodular forms have emerged mostly in the study of gravity and string theory [8]. Furthermore, we must note that the Bianchi-IX model is a polemic system.

Modular Forms are a special type of function that allows mathematicians to find deep and useful links between widely different fields of mathematics--complex analysis, number theory, group theory, topology, algebra, geometry, differential equations, string theory, cryptography, and others.

1 Introduction to Modular Forms 13 Applications of Modular forms To apply (quasi-)modular forms to the context of Mirror Symmetry, we need to use a slightly different definition of quasi-modular forms, which is to be found in [12].

Definition 7. Let Γ be a finite index subgroup of P SL2 Z as in definition 1. For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who has revised it substantially for the English edition.

It sets out to provide the reader with the basic knowledge of elliptic modular forms necessary. The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3(X).

We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi Cited by: Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem.

Noriko Yui, Helena Verrill, and Charles F. Doran. Modular Forms and String Duality. American Mathematical Society. p. 9. ISBN External links.