Date: Tuesday, October 08, 2013
Title: The solution to Siegel's Problem on small covolume lattices
Abstract: We outline the history and the proof of the identification of the minimal covolume lattice of hyperbolic 3space as the 353 Coxeter group extended by the involution preserving the symmetry of this diagram. This solves (in three dimensions) the problem posed by Siegel in 1945 (Siegel solved this problem in two dimensions by deriving the signature formula identifying the (2,3,7)triangle group as having minimal coarea). There are strong connections with arithmetic hyperbolic geometry in the proof and the result has applications in the maximal symmetry groups of hyperbolic 3manifolds (in much the same way that Hurwitz 84g84 theorem and Siegel's result do).
Speaker: Gaven Martin
Institution: Massey University
