Domain exchange transformations (DETs) are dynamical systems of piecewise translations defined on piecewise smooth Jordan domains. DETs are two-dimensional generalizations of interval exchange transformations which …
Convex polyhedra is an attractive and fundamental subject in which geometry is nicely joined with combinatorics and topology. My thesis studies convex polyhedra from two …
A $(p,q,r)$-complex hyperbolic triangle group is a group generated by complex reflections across complex geodesics meeting at angles $\pi/p, \pi/q, \pi/r$. In this thesis, we …