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.
 

Film featuring the work of the SFB

"The Discrete Charm of Geometry"
 

Next Seminars

SFB Colloquium
  • 12.03.2024, 14:15 - 15:00
  • 14:15 - 15:00 Constant mean curvature surfaces, Fuchsian systems and multiple zeta values, Sebastian Heller (Beijing Institute for Mathematical Sciences and Applications)
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  • Minimal (CMC) surfaces are critical points of the area functional (with fixed enclosed volume) and characterized by vanishing (constant) mean curvature. In my talk, I will explain how minimal and CMC surfaces in the 3-sphere can be described using monodromy data. In the case of concrete examples like the Lawson and Karcher-Pinkall-Sterling surfaces, these monodromy data lead to families of Fuchsian systems whose coefficients can be computed iteratively in terms of (alternating) multiple zeta values like \zeta(3). I will show how to extract geometric quantities like the area and the enclosed volume from the monodromy data. As an important application of this approach, the areas of the Lawson surfaces \xi_{1,g} are shown to be strictly monotonic in their genus g. This talk is based on joint work with L. Heller and M. Traizet.
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