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
- 28.06.2022, 14:15 - 15:15
14:15 - 15:15
Semi-discrete pluri-Lagrangian structures and the Toda hierarchy,
Mats Vermeeren (University of Leeds)
- The first part of this talk will be an introduction to pluri-Lagrangian systems (Lagrangian multiforms) in the context of continuous integrable systems. The role of a Lagrange function in this theory is played by a differential d-form in a higher-dimensional multi-time, which describes the system of interest together with its symmetries. I will highlight some appealing features of this approach and connections to more common notions of integrability. In the second part I will present the newly developed theory of semi-discrete Lagrangian 2-forms. The main example will be the Toda lattice and the hierarchy of ODEs which it is part of. There is more to this hierarchy than meets the eye: by constructing a semi-discrete Lagrangian 2-form, we will find a hierarchy of PDEs hiding within.
- Closing Date: 30.06.2022
- Location: TU Berlin
- Type: Studentische Hilfskraft
- Closing Date: 12.04.2023
- Type: Fellowship