The Condition Number of a Random Matrix: From von Neumann-Goldstine to Spielman-Teng

Van Vu
Rutgers, The State University of New Jersey
September 27, 2010

The condition number of a matrix is at the heart of numerical linear algebra. In the 1940s von-Neumann and Goldstine, motivated by the problem of inverting, posed the following question:

(1) What is the condition number of a random matrix ?

During the years, this question was raised again and again, by various researchers (Smale, Demmel etc). About ten years ago, motivated by "Smoothed Analysis", Spielman and Teng raised a more general question:

(2) What is the condition number of a randomly perturbed matrix ?

Conspiracy Theories in Medicine

Didier Fassin, James D. Wolfensohn Professor, School of Social Science
Institute for Advanced Study
September 25, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools and Mathematics and Natural Sciences.

Quanta, Symmetry, and Topology

Frank Wilczek
Herman Feshbach Professor of Physics, Massachusetts Institute of Technology
September 24, 2010

Quantum theory radically transforms our fundamental understanding of physical reality. It reveals that the world contains a hidden richness of  structure that we have barely begun to control and exploit. In this lecture, Frank Wilczek indicates the extraordinary potential ofquantum engineering (the size and nature of Hilbert space); reviews one important ongoing effort to harness it (topological quantum computing); and speculates on its ultimate prospects (quantum minds).

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools of Mathematics and Natural Sciences.