- Affiliation: TU Berlin
- Web Site: https://page.math.tu-berlin.de/~bobenko/
- Email: bobenko [at] math.tu-berlin.de
- Title: Structure preserving discretizations: Towards generalizations of conformal maps and circle patterns
- Date & room: Tuesday, 4th July at 9:00 - 10:00 (Room: San Salvatore)
Structure-preserving discretization in the field of geometry is the paradigm of discrete differential geometry. Here, of course, deciding which of the structures are to be taken into account is a nontrivial problem. In some aspects, the discrete theory turns out to be even richer than its smooth counterpart. It focuses on developing constructive methods, which allow one to prove natural existence and uniqueness results, as well as the corresponding convergence statements. The well-established theory of discrete conformal maps and circle patterns has already found numerous applications in geometry processing. We present their generalizations beyond the conformal limit: decorated discrete conformal maps and ring patterns, which share the corresponding existence and uniqueness statements. The theory and construction methods are based on variational principles. We also briefly explain how structure preserving discretizations recently helped to answer the long-standing question whether a surface in three-space is uniquely determined by its metric and curvatures (Bonnet problem).
Alexander Bobenko is a professor of mathematics at the Technical University Berlin, where he currently leads the DFG Collaborative Research Center "Discretization in Geometry and Dynamics". He earned his PhD in mathematical physics in 1985 from Steklov Mathematical Institute, St. Petersburg. Following his studies, he received the Alexander von Humboldt Foundation Fellowship and spent two years as a postdoc in Bonn and Berlin. Alexander is interested in differential geometry, dynamical systems and mathematical visualization. His publications include books and numerous papers in geometry and mathematical physics. He also produced documentary and animation films. During the last years his main interest has moved to discrete differential geometry, a mathematical area which aims to develop and apply discrete analogs of the notions and methods of differential geometry.