Discretization in Geometry and Dynamics
SFB Transregio 109


The SFB/TRR 109 "Discretization in Geometry and Dynamics" has been funded by the Deutsche Forschungsgemeinschaft e.V. (DFG) since 2012. 
The project is a collaboration between:

The central goal of the SFB/Transregio is to pursue research on the discretization of differential geometry and dynamics. In both fields of mathematics, the objects under investigation are usually governed by differential equations. Generally, the term "discretization" refers to any procedure that turns a differential equation into difference equations involving only finitely many variables, whose solutions approximate those of the differential equation.

The common idea of our research in geometry and dynamics is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. If we refine the discrete models by decreasing the mesh size they will of course converge in the limit to the conventional description via differential equations. But in addition, the important characteristic qualitative features should be captured even at the discrete level, independent of the continuous limit. The resulting discretizations constitutes a fundamental mathematical theory, which incorporates the classical analog in the continuous limit.

The SFB/Transregio brings together scientists from the fields of geometry and dynamics, to join forces in tackling the numerous problems raised by the challenge of discretizing their respective disciplines.

New film featuring the work of the SFB

"The Discrete Charm of Geometry"

Next Seminars

SFB Colloquium
  • 23.05.2017, 15:30 - 16:30
  • 15:30 - 16:30 (@TUM) A theoretical framework for the analysis of Mapper, Mathieu Carrière (INRIA France)
  • Mapper is probably the most widely used TDA (Topological Data Analysis) tool in the applied sciences and industry. Its main application is in exploratory analysis, where it provides novel data representations that allow for a higher-level understanding of the geometric structures underlying the data. The output of Mapper takes the form of a graph, whose vertices represent homogeneous subpopulations of the data, and whose edges represent certain types of proximity relations. Nevertheless, the inherent instability of the output and the difficult parameter tuning make the method rather difficult to use in practice. This talk will focus on the study of the structural properties of the graphs produced by Mapper, together with their partial stability properties, with a view towards the design of new tools to help users set up the parameters and interpret the outputs.
  • more
Kis-Sem: Keep it simple Seminar
  • 26.05.2017, 14:00 - 15:00
  • 14:00 - 15:00 Pluecker geometry of ruled surfaces, Thilo Rörig 
  • more
Kis-Sem: Keep it simple Seminar
  • 30.05.2017, 14:00 - 15:00
  • 14:00 - 15:00 TBA, Isabella 
  • more
Job Opening

PhD Position in Mathematics (75%)
  • Closing Date: 26.05.2017
  • Location: TU Berlin
  • Type: Ph.D.
Current Guests and Visitors
  • Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 30.04.2018)
  • Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2016 - 31.03.2019)
Forthcoming Guests and Visitors
  • Prof. Dr. Franz Pedit as Guest Professor at TU Berlin (01.06.2017 - 31.12.2017)
  • Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (04.06.2017 - 17.07.2017)
  • Prof. Dr. Stephan Tillmann as Guest Professor at TU Berlin (18.07.2017 - 15.01.2018)