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

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 ?

## What if Current Foundations of Mathematics are Inconsistent?

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.

## Conspiracy Theories in Medicine

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.

## Geometry of Growth and Form: Commentary on D'Arcy Thompson

## Expansion in Linear Groups and Applications

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.

## Fundamental Physics in the Twenty-first Century

## Cosmology: Recent Results and Future Prospects

In this talk, Professor Matias Zaldarriaga discusses the development of the modern study of cosmology, beginning with the discovery of the expansion of the Universe by Edwin Hubble, through current efforts to map the cosmic microwave background, test ideas about the initial conditions of the Universe, and explain the accelerated expansion of the Universe.

## Quanta, Symmetry, and Topology

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.