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
- 22.01.2018, 15:00 - 15:45
15:00 - 15:45
(Exceptional date and time!)
Higher solutions of Hitchin's self-duality equations,
Sebastian Heller (Universität Tübingen)
- Solutions of Hitchin's self-duality equations correspond to special real sections of the Deligne-Hitchin moduli space - twistor lines. A question posed by Simpson in 1995 asks whether all real sections give rise to global solutions of the self-duality equations. An affirmative answer would allow for a complex analytic procedure to obtain solutions of the self- duality equations. The purpose of my talk is to explain the construction of counter examples given by certain (branched) Willmore surfaces in 3-space (with monodromy) via the generalized Whitham flow. Though these higher solutions do not give rise to global solutions of the self- duality equations on the whole Riemann surface M, they are solutions on an open dense subset of it. This suggest a deeper connection between Willmore surfaces, i.e., rank 4 harmonic maps theory, with the rank 2 self-duality theory. The talk is based on joint work with L. Heller.
- 23.01.2018, 13:30 - 14:00
13:30 - 14:00
Introduction to the talk "Euler-Arnold theory for SPDEs",
- 23.01.2018, 14:15 - 15:15
14:15 - 15:15
(Live broadcast from TU Berlin to TU München)
Euler-Arnold theory for SPDEs?,
Alexander Schmeding (TU Berlin)
- In 1966 V. Arnold demonstrated that Euler's equations for an ideal fluid can be understood as the geodesic equation on the group of volume preserving diffeomorphisms with respect to a suitable Riemannian metric. Subsequently this bridge between PDEs on finite dimensional manifolds and ODEs on infinite-dimensional manifolds has been used to study the so called Euler-Arnold equations (e.g. Ebin/Marsden 1970).
In this talk we will give a short tour to this theory and its key ideas. Our aim is to discuss a possible extensions of these techniques to certain SPDEs which have recently been considered in Fluid dynamics (Crisan, Flandoli, Holm 2017).
This is joint with K. Modin (Chalmers, Gothenburg) and M. Maurelli (TU Berlin).
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. Wolfgang K. Schief as Guest Professor at TU Berlin (26.11.2017 - 20.02.2018)
Forthcoming Guests and Visitors
- Dr. Sebastian Heller as Visitor at TU Berlin (22.01.2018 - 23.01.2018)
- Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
- Associate Prof. Shimpei Kobayashi as Visitor at TU München (01.04.2018 - 14.06.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU Berlin (15.06.2018 - 14.08.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU München (15.08.2018 - 21.09.2018)