MathMeetings.net

Arithmetic groups provide a fruitful link between various areas, such as geometry, topology, representation theory and number theory. Methods from geometry and topology hinge on the fact that arithmetic groups are lattices in Lie groups, whereas the theory of automorphic forms establishes a connection to representation theory and number theory. This interplay is especially intriguing in the setting of hyperbolic 3-manifolds. Indeed many conjectures in 3-manifold theory tend to be much more accessible for hyperbolic 3-manifolds whose fundamental groups are arithmetic, and conversely such manifolds provide the simplest set-up in which some of the most exciting new phenomena in the Langlands program can be studied. This conference will bring together researchers with various backgrounds around links between number theory and 3-manifolds. Central topics of the conference are the cohomology of arithmetic groups, the relation between torsion and L²-torsion, profinite invariants of 3-manifolds, and number theoretic ramifications.