An Introduction to the AMS-NZMS Maclaurin Lecture: Siegel's Problem in Three Dimensions

Gaven J. Martin
2016 Notices of the American Mathematical Society  
We discuss our recent solution to Siegel's 1943 problem concerning the smallest co-volume lattices of hyperbolic 3-space. O ver the last few decades the theory of Kleinian groups-discrete groups of isometries of hyperbolic 3-space-has flourished because of its intimate connections with low-dimensional topology and geometry and has been inspired by the discoveries of W. P. Thurston. The culmination must certainly be Perelman's proof of Thurston's geometrisation conjecture, which states that
more » ... ch states that compact 3-manifolds can be decomposed canonically into pieces that have
doi:10.1090/noti1467 fatcat:pdmy665cuja4vkjmwix2m36xgm