# Recently Added

## The Fundamental Curve of p-Adic Hodge Theory

## Descriptions of the Grain-Growth Structure

## Overview of the p-Adic Local Langlands Correspondence for $GL(2,Q_p)$

(Introduction to the Lecture Series and and overview for those unable to attend the whole Lecture Series)

## Galois Representations and Automorphic Forms

## The Completed Cohomology of Arithmetic Groups

## The Completed Cohomology of Arithmetic Groups

## High-Rate Codes with Sublinear Time Decoding

## 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 ?

## Invariance Principles in Theoretical Computer Science

In this talk I will insult your intelligence by showing a non-original proof of the Central Limit Theorem, with not-particularly-good error bounds. However, the proof is very simple and flexible, allowing generalizations to multidimensional and higher-degree invariance principles. Time permitting, I will also discuss applications to areas of theoretical computer science: property testing, derandomization, learning, and inapproximability.