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Friday, September 7, 2012

Analysis Seminar
2:00 pm   in 241 Altgeld Hall,  Friday, September 7, 2012
 Del Edit Copy
Submitted by aimo.
 Gaven Martin (Massey University, New Zealand)The solution to Siegel's ProblemAbstract: We outline the history and the proof of the identification of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3 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 co-area. There are strong connections with arithmetic hyperbolic geometry in the proof and the result has applications in the maximal symmetry groups of hyperbolic 3-manifolds (in much the same way that Hurwitz 84g-84 theorem and Siegel's result do).