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.
New film featuring the work of the SFB
- 07.02.2017, 14:15 - 16:30
14:15 - 15:15
Orientational order on surfaces - the coupling of topology, geometry and dynamics,
Axel Voigt (TU Dresden)
- We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite-element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincare-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.
15:30 - 16:30
Fred Chazal (INRIA France)
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)
- Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (27.06.2016 - 20.02.2017)