#
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.

Papers arising from the workshop: