Discrete differential geometry - integrable discretization
A key research area in discrete differential geometry is "integrable discretizations".
Instead of attempting to approximate a smooth theory by a (fine enough) discretiziation, the idea in integrable discretizations is to create an independent discrete theory that is used to model the problem at hand.
This approach has several advantages, from highly efficient numerical algorithms that seem to be very stable also in long term or asymptotic behaviour, to a deeper understanding of the integrable nature of the smooth theory being discretized.
The lectures will give an introduction to basic ideas of integrable discretization, an outline of some key methodology and of the problems to be solved on the way; to elucidate the presented concepts some particular classes of smooth/discrete surfaces will be discussed in detail in the second part of the lectures. Then, students will prepare presentations on smooth and discrete geometries in pairs/groups, based on classical references and recent research articles.