2009;
292 pp;
Softcover

MSC: Primary 00;

**Print ISBN: 978-0-8218-4885-2
Product Code: MBK/67**

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

**Electronic ISBN: 978-1-4704-1602-7
Product Code: MBK/67.E**

List Price: $41.00

AMS Member Price: $32.80

MAA Member Price: $36.90

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#### Supplemental Materials

# Poincaré’s Legacies, Part II: pages from year two of a mathematical blog

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*Terence Tao*

There are many bits and pieces of folklore in mathematics that are
passed down from advisor to student, or from collaborator to
collaborator, but which are too fuzzy and non-rigorous to be discussed
in the formal literature. Traditionally, it was a matter of luck and
location as to who learned such folklore mathematics. But today, such
bits and pieces can be communicated effectively and efficiently via the
semiformal medium of research blogging. This book grew from such a blog.

In 2007, Terry Tao began a mathematical blog to cover a variety of
topics, ranging from his own research and other recent developments in
mathematics, to lecture notes for his classes, to non-technical puzzles
and expository articles. The articles from the first year of that blog
have already been published by the AMS. The posts from 2008
are being published in two volumes.

This book is Part II of the second-year posts, focusing on geometry,
topology, and partial differential equations. The major part of the
book consists of lecture notes from Tao's course on the Poincaré
conjecture and its recent spectacular solution by Perelman. The course
incorporates a review of many of the basic concepts and results needed
from Riemannian geometry and, to a lesser extent, from parabolic PDE.
The aim is to cover in detail the high-level features of the argument,
along with selected specific components of that argument, while
sketching the remaining elements, with ample references to more complete
treatments. The lectures are as self-contained as possible, focusing
more on the “big picture” than on technical details.

In addition to these lectures, a variety of other topics are discussed,
including expository articles on topics such as gauge theory, the Kakeya
needle problem, and the Black–Scholes equation. Some selected comments
and feedback from blog readers have also been incorporated into the
articles.

The book is suitable for graduate students and research mathematicians
interested in broad exposure to mathematical topics.

#### Readership

Graduate students and research mathematicians interested in mathematics in general with a focus on geometry, topology, and partial differential equations.

#### Reviews & Endorsements

Most of [the articles] are connected in one way or another with Tao's research interests, so if you have research interests that overlap with those of Tao, then it is a great pleasure to read ... Given how broad Tao's research interests are, that applies to just about everyone.

-- Mathematical Reviews