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
Next SFB Workshop
- 04.10. - 06.10.2017
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.
- 22.08.2017, 14:15 - 15:15
14:15 - 15:15
Cerf theory for graphs,
Max Krause (FU Berlin)
- Following the 1998 paper by Karen Vogtmann and Allen Hatcher, we study a deformation theory for families of pointed marked graphs with fixed fundamental group, inspired by established Cerf theory for smooth functions on manifolds. We will explain how these notions translate to the setting of pointed marked graphs and give an outlook on a basic application – a stability proof for the rational homology of the automorphism group of the free group with n generators.
- 29.08.2017, 14:15 - 15:15
14:15 - 15:15
An introduction to the Riemannian Geometry of Orbifolds,
Christodoulos Savva (Imperial College London)
- Manifolds are locally modelled on R^n. In the same sense, orbifolds are locally modelled on R^n modulo a finite group action. By introducing a Riemannian metric on orbifolds we have the generalization of various results like Bonnet-Myers and Synge's theorems. We will discuss some fundamental concepts, examples of low-dimensional orbifolds and some of these generalized theorems.
- 24.10.2017, 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.
- Closing Date: 31.08.2017
- Location: TU Berlin
- Type: Ph.D.
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. Franz Pedit as Guest Professor at TU Berlin (07.06.2017 - 31.12.2017)
- Prof. Dr. Stephan Tillmann as Guest Professor at TU Berlin (18.07.2017 - 15.01.2018)
Forthcoming Guests and Visitors
- Christodoulos Savva as Visitor at TU Berlin (28.08.2017 - 29.08.2017)
- Prof. Dr. Anna Felikson as Visitor at TU Berlin (10.09.2017 - 21.09.2017)