Arithmetic geometry of orthogonal and unitary Shimura varieties (12w5011)

The Banff International Research Station will host the "Arithmetic geometry of orthogonal and unitary Shimura varieties" workshop from June 3rd to June 8th, 2012.

One of the main occupations of number theory is the solution of polynomial equations. It is a well-known phenomena that in general such solutions can only be found in number systems that are larger than the integers and their fractions. The creation and understanding of such number systems can be done with great success using the theory of complex multiplication. This theory uses recent advances in the understanding of representation of groups and also about the manifolds associated with them (the symmetric spaces). Much progress has been made in this area in recent years due to the discoveries of Brocherds and the development of the arithmetic and geometry of Shimura varieties (objects derived from the symmetric spaces). The workshop is devoted to presenting the state of the art in this subject and mapping further topics of central importance.

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).