Convex Algebraic Geometry (10w5007)


(Universitat Konstanz)

(University of California Berkeley)

(University of Washington)


The Banff International Research Station will host the "Convex Algebraic Geometry" workshop from February 14th to February 19th, 2010.

Many geometric objects arising naturally in nature, science or engineering possess two
desirable properties. They are convex and semialgebraic. Convex sets have the property
that one can move between any two of its points along a straight line without leaving
the set. Semialgebraic sets can be described combining polynomial inequalities by easy
logical operations. The areas of mathematics primarily investigating these objects are
Convex Analysis and Real Algebraic Geometry, respectively. Both convexity and a
semialgebraic description can be exploited algorithmically, however in totally different
ways and with huge restrictions. Convexity can lead to very fast numerical algorithms for
navigating on a geometric object. For these algorithms to work, one needs however additional
structure, for example in form of a nicely represented barrier. Semialgebraic sets can
in principle be dealt with on a computer. Very general symbolic algorithms are known
to investigate and handle them. However, these algorithms are often not efficient enough for practical purposes. Recently, some corner stones have been laid to take advantage of both
features at the same time. We propose that the corresponding scientific communities join
forces to create a new subject called Convex Algebraic Geometry.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).