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Discretization in Geometry and Dynamics
SFB Transregio 109

 

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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 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

"The Discrete Charm of Geometry"
 

Next SFB Workshop
SFB Workshop 2023 "DGD Days"
  • 18.09. - 22.09.2023
  • The annual DGD Days on "Discretization in Geometry and Dynamics" will be held this year in the Science and Study Center of the TU München, located in the former Cistercian Monastery of Raitenhaslach in Bayern. The DGD Days program is organized with presentations of key themes in the mornings and with workshops and research exchange groups in the afternoons, providing ample opportunity for discussion and exchange.
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Next Seminars
SFB-Seminar Berlin
  • 06.06.2023, 14:15 - 15:15
  • 14:15 - 15:00 (H-Café) Planar networks and simple Lie groups, Anton Izosimov (U Arizona)
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  • Elements of the matrix group GL(n) can be encoded by weighted planar networks (directed graphs with numbers written on edges) with n sources and n sinks. Such graphical representation is useful for studying matrix factorizations, totally positive matrices etc. Furthermore, Gekhtman, Shapiro, and Vainshtein showed that such networks also capture Poisson geometry of GL(n) endowed with a standard multiplicative Poisson bracket. In the talk I will present a similar graphical representations of simple Lie groups of type B and C.
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SFB Colloquium
  • 27.06.2023, 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.
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SFB Colloquium
  • 11.07.2023, 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.
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