Department of Mathematics
Title : The solution to Siegel's problem
| Speaker: Professor Gaven Martin Affiliation: Massey University Time: 3:00 pm Thursday, 18 April, 2013 Location: MLT3 |
Abstract
| 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 identifying three-dimensional analogues of Hurwitz's 84g-84 theorem as Siegel's result do. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
