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 Technische Universität Berlin as lead university,
- the Technische Universität München as partner university,
- and individual scientists from
- the Freie Universität Berlin,
- the Humboldt Universität Berlin,
- the Universität Potsdam,
- the Ludwig-Maximilians-Universität München,
- the Institut of Science and Technology, (Austria)
- the Technische Universität Wien, (Austria) and
- the Technische Universität Graz (Austria).
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.
Film featuring the work of the SFB
Next SFB Workshop
Young Investigators Workshop 2023
- 12.04. - 14.04.2023
From April 12th-14th 2023 the SFB/TRR 109 will hold a "Young Investigators Workshop" in Weimar. The workshop is open to SFB members at the PhD and Post-Doc level only, and offers the opportunity for young investigators to discuss mathematics, careers, and other aspects of academic life in a relaxed, collegial atmosphere.
- 29.03.2023, 15:15 - 16:15
15:15 - 16:15
The Geometry of Discrete AGAG-Webs in Isotropic 3-Space,
Christian Müller (TU Vienna)
- We investigate webs from the perspective of the geometry of webs on surfaces in three dimensional isotropic space. Our study of AGAG-webs is motivated by architectural applications of gridshell structures where four families of manufactured curves on a curved surface are realizations of asymptotic lines and geodesic lines. We describe all discrete AGAG-webs in isotropic space and propose a method to construct them. Furthermore, we prove that some sub-nets of an AGAG-web are timelike minimal surfaces in Minkowski space and can be embedded into a one-parameter family of discrete isotropic Voss nets. This is a joint work with Helmut Pottman.
Special Fellowships for Mathematicians from Ukraine
- Closing Date: 12.04.2023
- Type: Fellowship