Abstract Books

This volume contains the following:

- First, we get a "Previously in SiP", a short recap of what happened in previous issues.

- # 50 "Backlash": The next morning... We learn that Terry can be quite a tease! We learn more about Casey, Francine's mood swings and Katchoo's frustrations. Meanwhile, in Japan, Tambi gets a proposal from David...

- # 51 "What I want" (My Maiden Voyage): Francine can't seem to make up her mind and Katchoo's beginning to get tired of it... Poor David.. I hope he can handle Tambi..

- #52 "What I dream": It looks like it's therapy time for Francine! We learn more about Katchoo's feelings(beautifully done by Mr. Moore) and we meet our own duck hunter!

- #53 "What I got": It seems that Francine has finally made up her mind about what she wants, but may it be too late?

- #54 "Fields of Gold": What is going on with Ms Noel? Poor David... My heart is breaking for him... Oops, it seems like Katchoo has really done it this time... Francine returns to what's familiar.

This volume gets my highest recommendation!

Based on a long series of will abstracts that appeared over a period of 45 years in The New England Historical and Genealogical Register, this work encompasses what amounts to the first 30 years or so of the Suffolk County, Massachusetts, estate records (1640-1670). Altogether, the series refers to some 12,000 persons with regard to family relationships.

Since this series of abstracts appeared in more than 60 issues of the Register, it has remained obscure and out of reach of the customary researcher. The virtue of this volume is that it gathers up the various installments and makes them accessible via an added index of names.

Genealogists researching the period 1640 to 1670 will find this a useful and informative reference tool, especially since some of the original Suffolk County wills are no longer available.

Gail Levin did a great job explaining the American avant-garde art movement known today as Synchromism. It is beautifully illustrated, and it covers other modernist artists who used color for expression in addition to Morgan Russell and Stanton MacDonald-Wright. As a foremost buyer of paintings by Morgan Russell and Stanton MacDonald-Wright, I highly recommend this book. www.LawrenceBeebe.com

This is *the* reference for symmetric functions and related topics. The second edition is greatly expanded, including (among other things) valuable material on Macdonald polynomials (though the author modestly does not refer to them by this term). The exposition is clean and to the point, as we have come to expect of Macdonald. The only defect of the book is that it can be hard to find things in it. The index is much too short, and much of the material is presented in long lists of disconnected "examples" that are very hard to search through quickly.

It is the beginning of the Third Season of the Walt Disney Concert Hall as the home of the Los Angeles Philharmonic and a reminder to again study the conceptual emergence of Frank Gehry's architectural masterpiece. SYMPHONY: FRANK GEHRY'S WALT DISNEY CONCERT HALL is as fine a way to understand why all the magic happens as any book on his work and about this building in particular.

Beautifully illustrated, this takes us from the origin of Gehry's idea, the various sketches, renderings and models, the ground breaking ceremonies, then the gradual rising of the skeleton of the support system to the wrapping of the sculpture in various glazes of steel and glass, to the finished product. Each stage is extraordinary, mesmerizing, detailed and edifying.

Accompanying the work in progress are essays and commentary by acoustician Minoru Nagata, urban specialist Carol McMichael Reese, Frank Gehry, Deborah Borda and Conductor Esa-Pekka Salonen and enhance the majestic photography by Grant Mudford.

But as with all descriptive books, all written and photographic comments, the truth is in the final result: the quality of sound and spiritual experience of live orchestral and choral music in the hall is paramount. And it is now, after two seasons and beginning its third that the proof is in the hearing. This is one of the most acoustically perfect places to experience music in the world. Composers (including Salonen in 'Wing on Wing') continue to be inspired to write commissioned works that reveal ever more extensive attributes of the space. The third season opened with Magnus Lindberg's 'Sculpture - The LA Project', a work for huge orchestra minus first violins but including two pianos, the great organ, extensive percussion section, and expanded deep voices in all the sections, and the effect was dazzling.

This book is a must for music lovers, architecture admirers, and for both those who are still wondering how this miracle happened as well as those planning to visit Los Angeles to hear and see for themselves. Highly recommended. Grady Harp, October 05

A wonderful history of the woman's periodical in early America: what was being written, for whom, and the effects of their rhetoric. Nice to be able to read about the progression, sometimes regression, of the woman's magazine. Food for thought about the changes, foci, and agendas of today's women's magazines: should there be less, not more, advertising? Should there be more writing about "issues" of the day? This book will allow readers to reflect and consider.

Founded in 1960, the Tamarind Institute has had a major influence on art-making in this century, placing American lithographers at the forefront of printmaking efforts. This documents the Institute's achievements, following the artists and participants who've worked there for years and offering black and white and color reproductions of their works throughout. An excellent history.

The life and art of Esther Phillips is revealed in This Fantastic Struggle: The Life And Art Of Esther Phillips, a collection of letters, interviews, scholarly analysis, and insights on what it meant to be an artist during the Depression years and thereafter. A gorgeous centerfold display of a selection of her works accompanies pages of detail which are intricate and insightful, filled with drama and facts. The result is a comprehensive coverage of a lesser-known artist who deserves a place in history.

Many art lovers have no entry point to abstract modern art. It is bad enough to see a canvas filled with rising black lady fingers, or crowded with primary color matchsticks which look as if a child had drawn them. Even worse, if a huge, plain white canvas, or a black one, or a purple one is put in a frame, hung in a museum, and sold for thousands of dollars, we have no idea why. Frank Whitford finds a simple path through history, and through the evolving types of abstract art, to lead us by the hand into the thicket, show us what is going on in there and what it means, and bring us safely to the other side, educated and ready to go look at some pictures - more importantly, ready to look at the abstract pictures with new appreciation and understanding.

Whitford uses traditional pictures we all appreciate and understand to provide a strong starting point for the journey into the abstract.

Whitford's writing style is at once clear, erudite, educated, not without humor and irony, and always entertaining. He is never cynical or sarcastic, no matter how much this subject would seem to set up easy targets. Abstract art is serious business for those in the know, and this book gives us lay readers a chance to count ourselves in that group.

It performs a valuable service.

Physicists view vertex algebras in many different ways, depending on their area of research. Some have used them without calling them as such, such as those dealing with the quantum operator equations of motion in the Heisenberg picture for potentials of higher order than quadratic. Researchers in string theory will view them in the context of two-dimensional conformal field theory, and in the use of the ubiquitous Virasoro algebra. Those in quantum field theory/elementary particle physics come across them in the context of the operator product expansion.

Mathematicians view them in many different ways also. The exciting results in the construction of the Monster group by Richard Borcherds has an interpretation in the theory of vertex algebras. And, as the authors of this book point out, vertex algebras provide a rigorous formulation of two-dimensional conformal field theories. Most concepts in quantum field theory do not have such a rigorous formulation, and so any results that one can get in this regard are very useful to have.

This book gives a highly detailed overview of the theory of vertex algebras, so much so that the book is highly dense and requires long blocks of time for readers (such as this reviewer) who are not experts. However, even though the authors are mathematicians, they motivate the subject very well, instead of presenting a "definition-theorem-proof" format. Indeed, at the beginning of the book the authors give a very good summary of the theory and at the beginning of every chapter the authors inform the reader just what they are going to do in that chapter.

Loosely speaking, vertex operators can be viewed as generalizations of linear operators acting on a vector space, i.e. if V is a vector space, one can construct linear maps from V into the space of Laurent series with coefficients in V and from the space of bi-infinite Fourier series into the space of Laurent series with coefficients in V. One can also construct a bi-infinite formal series with coefficients in End(V) (the collection of endomorphisms of V), where these coefficients when acting on any element of V will vanish for large values of n. These different conceptions of a vertex operator are all equivalent, but the main issue at hand is the multiplication of vertex operators at the same point. The space End(V) is of course an associative algebra, and one can extend the products of elements of End(V) to the space of vertex operators via the "Wick product," a construction that is very familiar to those readers working in quantum field theory. All of these considerations are made rigorous in the first chapter of the book, wherein also the axioms for vertex algebras are given explicitly. Noted in these axioms is the presence of a `vacuum vector' in the vector space V, reflecting of course the connection of vertex operators with quantum field theory. The authors also point out that the axioms of a vertex algebra are natural generalizations of the axioms of an associative commutative algebra with a unit. When a vertex algebra happens to be commutative, it is essentially equivalent to a commutative algebra with a unit and a derivation.

The physicist reader will probably appreciate this book more than the mathematician reader, since, again, so many of the constructions have their place (albeit with a rigorous foundation) in physics. Indeed, vertex algebras appear as the chiral symmetry algebras of two-dimensional conformal field theories, such as the Heisenberg vertex algebra, which appears as the free bosonic theory; the Kac-Moody algebra, which appears as Wess-Zumino model, and the Virasoro algebra, appearing as the Belavin-Polyakov-Zamolodchikov minimal model. These are all vertex algebras that are associated to (infinite-dimensional) Lie algebras, and which are discussed in great detail in chapter two of the book.

The operator product expansion, again a familiar construction in quantum field theory, wherein the product of two fields at nearby points can be expanded in terms of other fields, is studied in chapter three. The most interesting fact that comes out of this chapter is the power of the locality axiom for vertex algebras, which allows the construction of a vertex operator from knowledge on how it acts on the vacuum vector. This is called the Goddard Uniqueness Theorem, and is proved in this chapter. The authors prove the associativity property of vertex algebras and give examples of the operator product expansion: the Heisenberg, Kac-Moody, and conformal vertex algebras.

The mathematician reader, especially one that is working the field of algebraic geometry, will not be disappointed in this book, as the authors connect vertex algebras with vector bundles and algebraic curves. In particular the authors show how to give a geometric realization to a vertex operator and consequently give a global geometric meaning to vertex operators on arbitrary algebraic curves. Central to this discussion is the notion of a conformal and more generally a quasi-conformal vertex algebra, and the action of a group of transformations on the vertex algebra that change coordinates by `internal symmetries.' This allows a coordinate-independent description of the vertex operation, and this is used to study spaces of coninvariants and conformal blocks associated with a quasi-conformal vertex algebra and a smooth projective curve. The conformal blocks form a vector space that give information on the algebraic curve, and the vector bundles on it. The authors spend a great deal of time discussing how the spaces of conformal blocks change as the complex structure on the curve changes. The authors do this by considering the space of conformal blocks as a sheaf on the moduli space of smooth pointed curves of some genus. This sheaf allows a kind of uniformization on the moduli space involving the action of the Lie algebra of derivations on this space. This is done both for Virasoro vertex algebras as well as affine Kac-Moody algebras. The book ends with a thorough discussion of chiral algebras, which give a coordinate-free approach to the operator product expansion on algebraic curves.