# Convex algebraic geometry, optimization and applications

September 21 to September 25, 2009

at the

American Institute of Mathematics, Palo Alto, California

organized by

William Helton and Jiawang Nie

## Original Announcement

This workshop will be devoted to the study of Convex Algebraic Geometry'' and some of its numerous applications. Convexity plays a fundamental role in mathematics, and its ubiquity in optimization makes it of crucial importance in many domains of application. In such situations, the geometric properties of convex sets are complemented by additional algebraic structure (e.g., the semialgebraic case, where sets are defined by means of polynomial inequalities). In this case, the rich interactions between the geometric, algebraic, and computational aspects are not yet well-understood.

Falling into this setting are classical linear programming (LP), the more recent area of semidefinite programming (SDP), and the associated linear matrix inequalities (LMI),which have had a major impact on engineering systems, combinatorial optimization and other areas. One focus of the workshop is the study (arising from linear systems engineering) of polynomials in matrices whose form does not depend on the size of the matrices; this requires development of a noncommutative semialgebraic geometry.

Convex Algebraic Geometry involves a healthy combination of real algebraic geometry, functional analysis, operator theory, convex optimization and several areas of application. We expect a diverse group with common emerging interests.

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.