Torsion in the homology of arithmetic groups: geometry, arithmetic, and computation (12w5075)


(Northwestern University)

(University of Massachusetts)

Akshay Venkatesh (NA)


The Banff International Research Station will host the "Torsion in the homology of arithmetic groups: geometry, arithmetic, and computation" workshop from July 1st to July 6th, 2012.

The Langlands program posits deep connections between two basic areas

of mathematics: number theory and analysis. The latter studies

continuous phenomena and forms the foundation of calculus. The

former, one of the oldest subjects in mathematics, studies the

patterns and geometry underlying prime numbers and their


One setting where both fields meet, and where concrete features of the

Langlands program can be seen, is that of arithmetic groups.

Arithmetic groups are certain highly symmetric structures that lead to

spaces with complicated geometry, spaces that in some sense give

geometric realizations of number-theoretic data. The Langlands

program makes some predictions about aspects of the geometry of these

spaces, but not about all, and computer experiments have shown that

these other aspects are necessarily part of the full picture. The

focus of this workshop is exploring these new connections between

geometry and number theory, with the hopes of revealing new structures

and building new collaborations between different groups of


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).