## STPM - p-Adic Galois Representations and $(\varphi,\Gamma)$-Modules

We will explain the equivalences between p-adic Galois representations and various types of $(\varphi,\Gamma)$-modules.

## STPM - Correlation Bounds for Polynomials

## STPM - The Cohomology of Arithmetic Groups

## STPM - The Structure of Materials

## STPM - Resolution of Singularities on Shimura Varieties, and the Local Langlands Correspondence

## 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.

## 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.