Iordan M. Iordanov

Presently I am a Ph.D. candidate, member of the research group GAMBLE.

I have the privilege of working with Monique Teillaud on my Ph.D. thesis titled Triangulations of Hyperbolic Manifolds. The goal is to formulate (both theoretically and practically) a robust and efficient method for computing Delaunay triangulations of 2D hyperbolic manifolds. Implementation will be inspired by and based on CGAL.

I obtained my Master's degree in Applied and Computational Mathematics from the University of Crete, Greece in 2015. I worked on my MSc thesis Shape-preserving interpolation on the sphere under the supervision of Menelaos Karavelas. Full text is available here. To our knowledge (at the moment of writing this paragraph), this is the first result in a similar setting---shape-preserving intrepolation in Euclidean 3D space has been treated in [1] and [2], but these are the first results on the unit sphere.

My Bachelor's degree is in Applied Mathematics, obtained from the University of Crete, Greece, in 2013. I worked on my BSc thesis The Euclidean InSphere Predicate under the supervision of Menelaos Karavelas. Full text is available here. The main result states that the InSphere predicate in 3D (corresponding to the InCircle predicate in 2D) can be evaluated by determining the sign of expressions of algebraic degree at most 10 in the input quantities. State-of-the-art results at the time of writing provided an upper bound for the algebraic degree of the InSphere predicate equal to 16.