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 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
- 03.12.2019, 14:15 - 16:30
14:15 - 15:15
Gromov's notion of 'partial differential relation' and applications: a tutorial,
Gero Friesecke (TU München)
15:30 - 16:30
Optimal Lattice Quantizers and Best Approximation in the Wasserstein Metric,
David Bourne (Heriot-Watt University, Edinburgh)
- In this talk I will discuss the problem of the best approximation of the three-dimensional Lebesgue measure by a discrete measure supported on a Bravais lattice. Here 'best approximation' means best approximation with respect to the Wasserstein metric W_p, p \in [1,\infty). This problem is known as the quantization problem and it arises in numerical integration, electrical engineering, discrete geometry, and statistics.
- 04.02.2020, 14:15 - 16:30
During the semester, the SFB TRR109 organizes a colloquium which takes place every four weeks. The organization of the colloquium alternates between the TU Berlin and the TU Munich. The presentations are broadcast live from the hosting university to the partner university.
Current Guests and Visitors
- Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 31.07.2020)
- Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
- Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2019 - 31.03.2021)