#
Theory and Algorithms of Linear Matrix Inequalities

August 1 to August 5, 2005
at the

American Institute of Mathematics,
San Jose, California

organized by

John Helton,
Pablo A. Parrilo,
and Mihai Putinar

## Original Announcement

This workshop will be devoted to
theoretical, practical and computational aspects of Linear Matrix
Inequalities. Arguably, the biggest revolution in linear control theory in
the 1990's has been the realization that most linear control problems
convert directly to matrix inequalities. These take the form of a
polynomial or rational function of matrices being positive semidefinite.
The last few years have witnessed a fruitful and quite unexpected
cross-polination, on this territory, of methods of real algebraic
geometry, operator algebras, optimization theory and computation theory.
The workshop will bring together experts working in each one of these
fields, with the aim of sharing their knowledge on a carefully selected
set of genuinely interesting and new mathematical problems. The workshop
will open very concrete possibilities of practical applications.
The main topics for the workshop are

- Inequalities in a free *-algebra
- Computational real algebra (commutative or not)
- Determinantal representations of non-commutative polynomials

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Positive polynomials in scalar and matrix variables, the spectral theorem and optimization

by J. William Helton and Mihai Putinar ,

*Operator theory, structured matrices, and dilations, 229-306, Theta Ser. Adv. Math., 7, Theta, Bucharest, 2007 * MR2389626