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Theta Functions–Bowdoin 1987, Part 1

About this Title

Leon Ehrenpreis and Robert C. Gunning, Editors

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 1989; Volume 49.1
ISBNs: 978-0-8218-1483-3 (print); 978-0-8218-9344-9 (online)
DOI: https://doi.org/10.1090/pspum/049.1

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Table of Contents

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Front/Back Matter

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Infinite analysis

• Takahiro Kawai – Systems of linear differential equations of infinite order: An aspect of infinite analysis [MR 1013121]
• Masaki Kashiwara and Takahiro Kawai – A particular partition of unity: an auxiliary tool in Hodge theory [MR 1013122]
• H. P. McKean – Is there an infinite-dimensional algebraic geometry? Hints from KdV [MR 1013123]
• Motohico Mulase – A correspondence between an infinite Grassmannian and arbitrary vector bundles on algebraic curves [MR 1013124]
• Mikio Sato – The KP hierarchy and infinite-dimensional Grassmann manifolds [MR 1013125]

Integrable systems

• Mark Adler – Some geometrical techniques in integrable systems [MR 1013126]
• N. Ercolani – Generalized theta functions and homoclinic varieties [MR 1013127]
• Shi Rong Lu – Explicit equations for the KP and MKP hierarchies [MR 1013128]
• Pierre van Moerbeke – Introduction to algebraic integrable systems and their Painlevé analysis [MR 1013129]
• Robert L. Sachs – Polynomial $\tau$-functions for the AKNS hierarchy [MR 1013130]
• Kanehisa Takasaki – Integrable systems as deformations of $\mathcal {D}$-modules [MR 1013131]

Kac-Moody algebras

• E. Arbarello, C. De Concini and V. G. Kac – The infinite wedge representation and the reciprocity law for algebraic curves [MR 1013132]
• Victor G. Kac and Minoru Wakimoto – Exceptional hierarchies of soliton equations [MR 1013133]
• Andrew Pressley and Vyjayanthi Chari – Unitary representations of some infinite-dimensional Lie algebras [MR 1013134]
• A. Rocha-Caridi – On highest weight and Fock space representations of the Virasoro algebra [MR 1013135]
• Gregg J. Zuckerman – Modular forms, strings, and ghosts [MR 1013136]

Lattice models

• Helen Au-Yang and Jacques H. H. Perk – Solution of Hirota’s discrete-time Toda lattice equation and the critical correlations in the $Z$-invariant Ising model [MR 1013137]
• Etsurō Date, Michio Jimbo, Tetsuji Miwa and Masato Okado – Solvable lattice models [MR 1013138]
• Atsuo Kuniba – Theta function identities in a series of solvable lattice models [MR 1013139]
• Jacques H. H. Perk – Star-triangle equations, quantum Lax pairs, and higher genus curves [MR 1013140]
• Craig A. Tracy – Introduction to exactly solvable models in statistical mechanics [MR 1013141]

Physics

• Michio Jimbo – Introduction to holonomic quantum fields for mathematicians [MR 1013142]
• Emil Martinec – Quantum field theory: a guide for mathematicians [MR 1013143]
• Yukihiko Namikawa – A conformal field theory on Riemann surfaces realized as quantized moduli theory of Riemann surfaces [MR 1013144]
• A. Neveu – The physics of string theory [MR 1013145]

Jacobian varieties

• Hershel M. Farkas – Schottky-Jung theory [MR 1013146]
• John Fay – Schottky relations on $\frac 12(C-C)$ [MR 1013147]
• R. C. Gunning – Analytic identities for theta functions [MR 1013148]
• John B. Little – Translation manifolds and the Schottky problem [MR 1013149]
• Henrik H. Martens – Mappings of closed Riemann surfaces [MR 1013150]
• José Ma. Muñoz Porras – Geometric characterization of Jacobians and the Schottky equations [MR 1013151]
• Emma Previato and George Wilson – Vector bundles over curves and solutions of the KP equations [MR 1013152]
• Roy Smith and Robert Varley – Deformations of singular points on theta divisors [MR 1013153]
• L. A. Takhtajan – Uniformization, local index theorem, and geometry of the moduli spaces of Riemann surfaces and vector bundles [MR 1013154]
• Noriaki Yamawaki – Explicit actions of the theta groups for theta divisors on Jacobian surfaces [MR 1013155]

Prym varieties

• Arnaud Beauville – Prym varieties: A survey [MR 1013156]
• Olivier Debarre – The trisecant conjecture for Pryms [MR 1013157]
• Vassil Kanev – Spectral curves, simple Lie algebras, and Prym-Tjurin varieties [MR 1013158]

Algebraic geometry

• Iacopo Barsotti – A new look for thetas [MR 1013159]
• L. Breen – The cube structure on the determinant bundle [MR 1013160]
• Michael D. Fried and Helmut Völklein – Unramified Abelian extensions of Galois covers [MR 1013161]
• William L. Hoyt – On twisted Legendre equations and Kummer surfaces [MR 1013162]
• A. B. Jijtchenko – On embedded tangent and secant varieties of projective algebraic varieties [MR 1013163]