# Category Archives for **Roots of polynomials**

## Lecture 5. Proof of Kadison-Singer (3)

This is the last installment of the proof of the Kadison-Singer theorem. After several plot twists, we have finally arrived at the following formulation of the problem. If you do not recall how we got here, this might be a … Continue reading

## Lecture 4. Proof of Kadison-Singer (2)

Recall that we are in the middle of proving the following result. Theorem. Let be independent random vectors in whose distribution has finite support. Suppose that Then with positive probability. Define the random matrix and its … Continue reading

## Lectures 2 and 3. Proof of Kadison-Singer (1)

The goal of the following lectures is to prove the following result about random matrices due to Marcus, Spielman, and Srivastava. This result readily implies a positive resolution of the Kadison-Singer conjecture, as was explained in detail in the previous … Continue reading

## Lecture 1. Introduction

The goal of our seminar this semester is to try to understand the unexpected application of the geometry of roots of polynomials to address probabilistic problems. Such methods have recently led to the resolution of several important questions, and could … Continue reading

## Fall 2014: Roots of polynomials and probabilistic applications

Welcome back to the stochastic analysis seminar! We resume this semester with an unusual but exciting topic: the geometry of roots of polynomials and their probabilistic applications. Understanding the roots of polynomials seems far from a probabilistic issue, yet has … Continue reading