math_groups_discgeom

ERC Advanced Grant Project

SDModels: Structured Discrete Models as a basis for studies in Geometry, Numerical Analysis, Topology, and Visualization

This project was successfully completed June 2015, after five years of intensive work, three very productive SDModels workshops, and lots of other activities. It has produced numerous successes, advanced the careers of the students and scientists involved, and produced a lot of output - a large part of this documented in scientific publications, many more papers are still under review and on the way to publication. We are happy for all the support and opportunities we had with this project, and grateful to ERC and its reviewers and administrators for making it possible. The work by SDModels is documented on these web pages. They will not be updated any more after December 2015: Please see the web pages of the scientists involved for their continuing work.

The research of the SDModels project has connected traditionally quite distant fields of current mathematical research via common or structurally similar discrete (mostly: geometric) models. We thus made substantial contributions to mathematical research, by highlighting, developing, and exploiting theory for common structures and structural similarities that occur in problems/theories from diverse mathematical application areas. This involved, in particular, the areas of

  1. Discrete Geometry
  2. Discrete Differential Geometry
  3. Mesh Generation/Numerics of PDEs
  4. Topology, Topological Combinatorics
  5. Simplicial Quantum Gravity

The work in the project was concentrated in three Focus Areas, namely
Focus Area 1: High-complexity Geometry
Focus Area 2: Delaunay Geometry: Polyhedral models with circle/sphere patterns
Focus Area 3: Topological connectivity and diameter of Discrete Structures

Third ERC "SDModels" Workshop March 23-26, 2015

at Freie Universität Berlin, for more details, see Events.

ERC

This project received funding from the European

Research Council under the European Union's Seventh Framework Programme

(FP7/2007-2013) / ERC grant agreement n° 247029