at the

American Institute of Mathematics, Palo Alto, California

organized by

John Helton, Pablo A. Parrilo, and Mihai Putinar

This workshop, sponsored by AIM and the NSF, 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

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

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