## The Pythagorean Theorem from another, slightly sophisticated, point of view

The Porcelli Lectures this year will be delivered by **Richard V. Kadison**, Kuemmerle Professor of Mathematics, at the University of Pennsylvania. His talks will center around operator algebras and the Pythagorean Theorem from another, slightly sophisticated, point of view.

### Lectures

**The Pythagorean Theorem: A Closer Look**- Tuesday, April 10, 2007, 3:40–4:30
**Operator Algebras: A Sampler**- Wednesday, April 11, 2007, 3:40–4:30
**The Pythagorean Theorem: An Advanced View**- Thursday, April 12, 2007, 3:40–4:30

All three lectures will take place in 130 Howe-Russell Geoscience Complex. Refreshments will be served in the Atrium in the Howe-Russell Geoscience Complex from 3:00 to 3:40.

### Abstract

Extensions and variants of the Pythagorean Theorem are presented, first from the point of view of finite-dimensional, linear algebra and, later, in the framework of infinite-dimensional Hilbert space. The results discussed make contact with the work of Kostant, Atiyah, and Guillemin-Sternberg in the convex geometry of symmetric spaces, the work of Horn and Schur on spectral theory, matrix inequalities, majorization, and convex polytopes, and semi-commutative, metric geometry from the point of view of conditional expectations. The first of the two Pythagoras lectures will be relatively elementary, the second will be slightly more advanced, relying somewhat on the operator-algebra, survey lecture that follows the first lecture.

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Poster.pdf | 2.05 MB |