My current research is heavily focussed on student progression through developmental mathematics. My Ph.D. thesis deals with factorization of isometries in hyperbolic 4-space. It was also partly an exposition on a wonderful paper by J. B. Wilker titled "Inversive Geometry" that approaches the study of Möbius transformations from a non-standard and (in my opinion) extremely useful point of view. Using his approach, we get some new techniques that enable us to "lift" from the Conformal Ball Model to the Hyperboloid Model of hyperbolic n-space. If you are interested in the study of hyperbolic geometry, John Ratcliffe's Foundations of Hyperbolic Manifolds is an excellent book on the subject. Maskit's Kleinian Groups and Beardon's Geometry of Discrete Groups are indispensable references as well.:Publications
Generating the Mobius Group with involution conjugacy classes (with Ara Basmajian), Proc. Amer. Math. Soc., 140 (2012), no. 11, 4011-4016. |