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
- 28.01.2020, 14:15 - 15:00
14:15 - 15:00
Cube flips in statistical mechanics and in planar geometry,
Paul Melotti (Université de Fribourg)
- An important property in the study of exactly solvable statistical models is the existence of a local transformation of the underlying graph and parameters, such that long range observables remain unchanged. This can often be seen as a "cube flip" (or star-triangle, or Yang-Baxter equation). On the other hand, there has been recently an intense line of research concerning canonical embeddings of such models, giving rise to "s-embeddings" related to the Ising model, "circle patterns" for the dimer model, and others. In this correspondence, local transformations of the model should be conjugated to theorems of planar (or projective) geometry on these embeddings. I will present a few cases of this correspondence, and of the following reciprocal question: can one find theorems of planar geometry that should be related to the local "flip" of such a model? This leads to the introduction of new classes of homogeneous quadrilaterals. This is based on a joint work in progress with Sanjay Ramassamy and Paul Thévenin.
- 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)