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Doctor of Philosophy, (Mathematics)
Study Completed: 2010
College of Sciences
Two elliptic generator kleinian groups
Kleinian groups have been studied for more than a century and have been reinvigorated with the recent work of Perelman and Thurston establishing the well known Poincaré conjecture. Ms Zhang''sthesis is a synthesis of geometry and topology using computational tools to study these groups in an important case. The collection of all such groups is described by a two-dimensional space with a fractal boundary. The computer assisted mathematical investigations in Ms Zhang’s thesis drew substantially on the theory of knots and revealed for the first time the size and the structure of the fractal boundary. The results of her study find important application in many areas and provide a conjecturally complete list of these groups in the most difficult case.
Distinguished Professor Gaven Martin
Professor David Gauld
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Last updated on Tuesday 04 April 2017