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Publisher:

Birkhäuser/Edizioni della Normale

Publication Date:

2006

Number of Pages:

57

Format:

Paperback

Series:

Publications of the Scuola Normale Superiore

Price:

24.95

ISBN:

978-88-7642-212-6

Category:

Proceedings

[Reviewed by , on ]

Fernando Q. Gouvêa

11/21/2007

As mathematics grows bigger and more complex, it becomes more and more important for mathematicians to tell others what is going on in their fields. This is, of course, the calling of colloquium speakers everywhere, and places where it is done particularly well (Séminaire Bourbaki, plenary lectures at the ICM, the AMS "Current Events" session at the Joint Mathematics Meetings, for example) earn everyone's admiration and, perhaps, gratitude.

It is no accident that the examples mentioned above involve not only giving a talk, but also writing and publishing it, making it accessible to the mathematical world at large. Most colloquia do not have this second life as written expository texts. The main reason for this, I suspect, is that it is far easier to give a good expository talk than it is to write an account of it that is precise, insightful, and understandable by a broad audience of mathematicians. New attempts at this should always be welcomed by the mathematical community, and so we welcome the first volume of articles from the Italian *Colloquium De Giorgi*, held at the Scuola Normale Superiore in Pisa.

There are always growing pains, I guess, and perhaps this explains how uneven this volume is. Some of the papers are little more than research announcements, stating a problem and announcing a couple of theorems. Lists of references range from a couple of pages to non-existent. Some pieces are far too brief, and read more like classroom notes than like a finished article.

The volume is beautifully made, printed on good paper and with an elegant cover. (It shares this feature with all of the volumes in the new *Edizione della Normale* series distributed by Birkhäuser.) The articles inside don't quite live up to the elegance of the package, but they deal with interesting mathematics, and several can be used as jumping-off points for those interested in learning more. I look forward to seeing the series grow and blossom.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and Editor of MAA Reviews.

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