# Free Analysis Seminar[ Edit ]

## Moderator: Orr Shalit

*Abstract:*

We will conclude our series of lectures on the paper "Dilations, LMIs, the matrix cube and beta distributions", presenting the proof that the commutability index equals the inclusion constant.

*Abstract:*

This is second lecture on the paper "Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions" by Helton, Klep, McCullough and Schweighofer.

*Abstract:*

We will resume our free analysis seminar (on Tuesdays during July) and go through parts of the paper "Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions" by Helton et. al.

All are invited. If you want to prepare for the seminar by reading requisite material please contact Orr Shalit (oshalit@tx)

*Abstract:*

This will be the third in a series of lectures in which we study the paper "Every convex free basic semi-algebraic set has an LMI representation" by Helton-McCullough (Annals of Math., 2012).

The main result is, roughly, that every convex free set defined by matrix valued polynomial inequalities has another representation - a Linear Matrix Inequality (LMI) representation, that is, it is given by matrix valued LINEAR inequailties.

*Abstract:*

This will be the second in a series of lectures in which we study the paper "Every convex free basic semi-algebraic set has an LMI representation" by Helton-McCullough (Annals of Math., 2012).

The main result is, roughly, that every convex free set defined by matrix valued polynomial inequalities has another representation - a Linear Matrix Inequality (LMI) representation, that is, it is given by matrix valued LINEAR inequailties.

*Abstract:*

We will start a series of lectures in which we will study the paper "Every convex free basic semi-algebraic set has an LMI representation" by Helton-McCullough (Annals of Math., 2012).

The main result is, roughly, that every convex free set defined by matrix valued polynomial inequalities has another representation - a Linear Matrix Inequality (LMI) representation, that is, it is given by matrix valued LINEAR inequailties.

*Abstract:*

We shall continue studying the question when are two LMI sets equal?We will give a detailed answer, in terms of unitary equivalence, and for the solution we will examine the Shilov boundary of an operator system inside a matrix algebra.