Randomization, Relaxation, and Complexity

The Banff International Research Station will host the "Randomization, Relaxation, and Complexity" workshop from February 28th to March 5th, 2010.

Whether it's the design of biomolecules or robots, or the study of physical phenomenae, solving equations is central in mathematics. However, while the underlying theory --- algebraic geometry --- goes back many centuries, it is only recently that algebraic geometry has begun to merge with more applied areas such as numerical analysis and optimization. This workshop aims to greatly advance this cross-pollenization by uniting recent techniques from computer science and algebraic geometry. Recent results have shown a close link between equation solving, the P=NP problem, and the Riemann Hypothesis. We are thus at a critical juncture where experts in several different communities can come together and make significant advances. In particular, while we now understand equations over the complex numbers well enough to make definitive statements and useful software, equation solving over the real numbers remains mysterious. This is where powerful ideas from randomization and approximation will come into play, and hopefully yield great advances

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).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif