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
- 24.05.2019, 12:00 - 13:00
12:00 - 13:00
Discrete mean curvature coordinates,
- 04.06.2019, 15:00 - 17:15
15:00 - 16:00
The Z-Dirac and massive Laplacian operators in the Z-invariant Ising model,
Béatrice de Tilière (University Paris Dauphine)
- This topic of this talk is Baxter's Z-invariant Ising model defined on isoradial graphs. We prove that certain key quantities of the model – the partition function, and edge-probabilities in the contour representation – can be explicitly expressed using the Z-massive Laplacian and its inverse, the massive Green function, introduced by Boutillier, dT, Raschel. This establishes a deep relation between classical 2d-models of statistical mechanics: the Ising model, spanning forests and random walk. In order to prove these results, we introduce the Z-Dirac operator; we relate it to the Z-massive Laplacian, extending to the full Z-invariant regime results obtained by Kenyon at the critical point; we then relate the Z-Dirac operator to the Ising model. The proof consists in establishing matrix relations allowing to compare matrix inverses and also, using additional arguments, determinants.
16:15 - 17:15
To be announced,
Nils Thürey (Technische Universität München)
- 07.06.2019, 12:00 - 13:00
12:00 - 13:00
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. Wolfgang K. Schief as Guest Professor at TU Berlin (01.05.2019 - 31.08.2019)
- Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2019 - 31.03.2021)