# 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

### Table of Contents

**Front/Back Matter**

**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]