My research falls into the broad area of Computer Graphics and Geometry. A significant part of my PhD research was the development of a generalized subdivision scheme for triangulations. It has exact geometric properties. More here. I am interested in all challenges that require the analysis of limit surfaces. Understanding the limit surface will help us to develop better algorithms for a wide variety of areas in Computer Graphics. The mathematical techniques used are of a wide variety including Optimization, Eigenvalue Optimization, Wavelets and Boxsplines and others. During my Diploma thesis in the area of Symplectic Geometry I learned all the background in Differential Geometry that is very helpful now.
Biermann, H., Grundel, S., Zorin D. "Subdivision schemes for surfaces with boundaries", in preparation.
Grundel, S.,Yu, T. "Multiresolution Analysis on a spherical domain
based on a flexible C2 subdivision scheme
over a valence 3 extraordinary vertex", submitted to Computer Aided Geometric Design, pdf
Grundel, S.(2011), "Eigenvalue Optimization in C2 Subdivision
and Boundary Subdivision", PhD Thesis NYU, pdf
Grundel, S.(2005), "Moment Maps and Diffeomorphism", Diploma Thesis ETH Zurich, pdf