Diophantine methods, lattices, and arithmetic theory of quadratic forms (11w5011)


(Wesleyan University)

Lenny Fukshansky (Claremont McKenna College)

(Universitaet des Saarlandes)

Jeffrey Vaaler (University of Texas at Austin)


The Banff International Research Station will host the "Diophantine methods, lattices, and arithmetic theory of quadratic forms" workshop from November 13th to November 18th, 2011.

In Diophantine geometry mathematicians investigate, following Diophantos of Alexandria from ancient Greece, the solutions to equations in several variables in integers and their analogues in other arithmetic situations using geometric methods; height functions are used to measure the size of solutions, and the theory of heights is an important branch of Diophantine geometry.

The arithmetic theory of quadratic forms originated as another branch of Diophantine geometry (the investigation of those equations which are quadratic in the variables), but over the last century evolved into an independent subject with its own problems and methods. These two lively areas of number theory have seen rapid development and spectacular successes over the recent years.

The goal of this workshop is to bring together leading experts and younger researchers working in these two fields, to emphasize the unification and interplay of these topics, and to promote interaction and exchange of ideas among researchers coming from North and South America, Europe, and Asia.

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).