New Topological Contexts for Galois Theory and Algebraic Geometry

Algebraic topology is primarily concerned with the introduction of computable or otherwise usable algebraic invariants of spaces and continuous mappings with a view to solving geometric problems. The oldest examples are derived from homotopy and homology of spaces, but the late twentieth century saw the subject expand rapidly and become increasingly sophisticated in its ability to define homotopically invariant algebraic machinery, often associated with multiplicative cohomology theories and their internal operations. The inputs to these have included established mathematical ideas from subjects such as algebraic geometry, number theory and many others. Our program is intended to bring together topologists actively developing or using these new techniques and to open further the interactions with other subject areas by including non-topologist participants who would contribute to this. The main focus is on new contexts for Galois theory and 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).

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