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
- 12.12.2017, 14:15 - 16:30
14:15 - 15:15
(@ TU München)
Combinatorial Solutions to Elastic Shape Matching,
Daniel Cremers (TU München)
- In my presentation, I will focus on four different shape matching problems, namely the matching between two planar shapes, the matching between two 3D shapes, the matching between a shape and an image and the matching between a planar and a 3D shape. In all cases, I will discuss combinatorial formulations for elastic shape matching and show how optimal or near-optimal solutions can be computed using dynamic programming or integer linear programming.
- 19.12.2017, 14:15 - 15:15
14:15 - 15:15
Orthogonal polynomials and the Painlevé equations,
Galina Filipuk (University of Warsaw)
- In this talk I shall review some of my recent results on the connection of recurrence relation coefficients of semi-classical-orthogonal polynomials to the solutions of discrete and differential Painlevé equations. I shall also briefly discuss multiple orthogonal polynomials.
- 09.01.2018, 14:15 - 16:30
14:15 - 15:15
Exact periodic stripes for minimizers of a local/non-local interaction functional in general dimension,
Eris Runa (MPI Leipzig)
- In this talk we will consider a functional consisting of a perimeter term and a non-local term which are in competition. In the discrete setting such functional was introduced by Giuliani, Lebowitz, Lieb and Seiringer. We show that the minimizers of such functional are optimal periodic stripes for both the discrete and continuous setting. In the discrete setting, such behaviour has been shown by Giuliani and Seiringer using different techniques for a smaller range of exponents. One striking feature of the functionals is that the minimizers are invariant under a smaller group of symmetries than the functional itself. In the continuous setting, to our knowledge this is the first example of a model with local/nonlocal terms in competition such that the functional is invariant under permutation of coordinates and the minimizers display a pattern formation which is one dimensional. This model has many similarities with the celebrated Ohta-Kawasaki functional. In particular for Ohta-Kawasaki functional, the minimality of periodic stripes is conjectured. This work is in collaboration with Sara Daneri.
15:30 - 16:30
Maximilian Engel (TU München)
- Closing Date: 11.12.2017
- Location: TU München
- Type: Ph.D.
- Closing Date: 31.12.2017
- Location: TU Graz
- Type: PostDoc
Current Guests and Visitors
- Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 30.04.2020)
- 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)
- Tetsuya Nakamura as Visitor at TU Berlin (04.09.2017 - 12.01.2018)
- Prof. Dr. Serguei Agafonov as Visitor at TU Berlin (22.11.2017 - 23.12.2017)
- Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (26.11.2017 - 20.02.2018)
- Prof. Dr. Peter Schröder as Guest Professor at TU Berlin (09.12.2017 - 19.12.2017)
Forthcoming Guests and Visitors
- Dr. hab. Galina Filipuk as Visitor at TU Berlin (18.12.2017 - 19.12.2017)
- Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)