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March 22, 2007

Matrix Door

There's a striking cover image on Rajendra Bhatia's Positive Definite Matrices (Princeton series in applied mathematics. Princeton, N.J.: Princeton University Press, 2007. Mathematics Library QA188 .B488 2007 Link to MNCAT record)

matrixdoor.jpg

This is credited on the back cover: "Doors of the Florence Baptistery show an example of a 4 x 7 matrix." Further investigation shows that these must be the gilded bronze North Doors, by Lorenzo Ghiberti (1404-24). Close-ups of the individual reliefs are available: North Doors, Florence Baptistry. The earlier south doors (by Pisano) are similarly structured, but the later east "Doors of Paradise" (also by Ghiberti) are a 2 x 5 matrix.

March 9, 2007

The tempo of Ricci flow

Bennett Chow, who recently left Minnesota for UC-San Diego and East China Normal University, has collaborated on another book on the Ricci flow, that hot topic involved in the attempts to prove the Poincaré conjecture:
Hamilton’s Ricci flow, by Bennett Chow, Peng Lu, and Lei Ni. Graduate studies in mathematics v. 77. Providence, R.I.: American Mathematical Society/Science Press, 2006. Mathematics Library QA670 .C455 2006 Link to MNCAT record

As implied by the series, it is accessible to graduate students. The previous book was aimed at researchers:
The Ricci flow: an introduction, by Bennett Chow and Dan Knopf. Mathematical surveys and monographs v. 110. Providence, R.I.: American Mathematical Society, 2004. Mathematics Library QA1 .M758x v.110 Link to MNCAT record

In explaining the difference between these "cousins," the authors compare the style of the 2004 book to jazz--"dive right into Ricci flow and then proceed at a metric pace, taking the time to appreciate the intricacies and nuances of the melody and structure of the mathematical music"--whereas the style of the 2006 book is more like rock 'n' roll--"after starting from more basic material, as a connection to Ricci flow, the tempo is slightly more upbeat. The recital is defined on a longer page interval, and consequently more ground is covered, with the intention of leading up to the forefront of mathematical research."

A further book is to appear in May: The Ricci flow: techniques and applications: Part I: Geometric Aspects, by Chow et al. Mathematical Surveys and Monographs v. 135. Providence, R.I.: American Mathematical Society, 2007.
Given the ten authors credited, perhaps its style will be orchestral.