Geometric Structures on Manifolds (12w5121)


(McMaster University)

Alexei Kovalev (University of Cambridge)

(University of California, Irvine)


The Banff International Research Station will host the "Geometric Structures on Manifolds" workshop from April 15th to April 20th, 2012.

Geometric Structures on Manifolds

In mathematics, topology describes the shape of things, and geometry describes the form or structure. The shape of an object can often be altered by deformation (stretching, shrinking or twisting), but its function, symmetry or stability will usually be changed in the process. An example of the relation between shape and structure is that of soap film spanning a curved wire frame. As the wire frame is twisted or bent, the soap film changes to fit the new structure.

On a dramatically larger scale, our current theories about the universe are based on Einstein's insights into the basic geometry and topology of space and time. The universe is "curved" due to forces of gravity between stars and planets, or near "black holes". However, this information alone is not enough to provide a full understanding of its "shape" or topology, which is the main problem in cosmology.

In this BIRS workshop, we are bringing together an international group of researchers in geometry and topology to investigate the central question: how is structure related to shape, or in mathematical terms, how are conditions on the geometry related to those of the underlying topology.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).