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Curriculum Vitae
A copy of my recent CV can be downloaded here: CV pdf file.
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Recent Preprints/Papers
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PhD Thesis of my student Ying Zhang
My student Ying Zhang successfully defended his PhD thesis in July 2004. The title is "Hyperbolic cone-surfaces, generalized Markoff maps, Schottky groups and McShane's Identity". You can download the pdf file here.
List of Selected Publications ( click here for full list of publications)
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Gallery of Images
These pictures arise from from recent joint work with Yasushi Yamashita where we study the dynamics of the action of the modular group PSL(2,Z) on the (relative) SL(2,C) character varieties of a one-holed torus (based on previous work with Y.L. Wong, Y. Zhang and S.P.K. Ng). The relative character varieties are determined by fixing the trace of the boundary curve on the torus. The pictures are produced by a computer program created by Yasushi Yamashita. Colored regions represent characters where the action of the modular group is proper and the black region represents characters where the action is not proper. When the action is proper, the orbit is controlled by a finite sub-tree of a infinite trivalent tree, the changes in the colors represent changes in the complexity of this finite tree. The size of the tree grows to infinity as one approaches the boundary of the colored regions.
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This series of pictures shows how the Maskit slice deforms as the boundary trace changes from -2+0i to -2+4i. The modular group acts properly discontinuously on the colored regions and the action is not proper on the black region.






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This series of pictures shows how the Maskit slice deforms as the boundary trace changes from -2+0i to -6+0i.






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This third series can be considered as deformations of the Riley slice again as boundary trace changes from -2+0i to -6+0i.






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This animation shows various slices of the relative SL(2,C) character varieties of a one holed torus, as the boundary trace changes from -2 to -6. The trace of a generator is fixed at 2+6i, the colored region represents characters for which the modular group acts properly, the black region represents characters for which the action of the mapping class group is not proper. The initial picture below corresponds (apparently, assuming a conjecture of B. Bowditch) to a slice of quasi-fuchsian space.

Click to see Animation
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Below are some interesting miscellaneous pictures obtained by varying parameters etc in the program of Yamashita:


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Tan Ser Peow
Department of
2,
mattansp (at) nus (dot) edu (dot) sg
(65) 6874-6160 (office)
(65) 6779-5452 (fax)
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Tan Ser Peow <mattansp (at) nus (dot) edu (dot) sg>
Last Modified: 23 May 2008.
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