Discretization in Geometry and Dynamics
SFB Transregio 109

 

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.
 

New film featuring the work of the SFB

"The Discrete Charm of Geometry"
 

Next Seminars

SFB-Seminar Berlin
  • 19.12.2017, 14:15 - 15:15
  • 14:15 - 15:15 Orthogonal polynomials and the Painlevé equations, Galina Filipuk (University of Warsaw)
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  • 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.
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SFB Colloquium
  • 09.01.2018, 14:15 - 16:30
  • 14:15 - 15:15 (@ TUM) Exact periodic stripes for minimizers of a local/non-local interaction functional in general dimension, Eris Runa (MPI Leipzig)
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  • 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 (@TUM) Local phenomena in random dynamical systems: bifurcations, synchronisation, and quasi-stationary dynamics, Maximilian Engel (TU München)
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  • We consider several related topics in the bifurcation theory of random dynamical systems: synchronisation by noise, noise-induced chaos and qualitative changes of fi nite-time behaviour. We study these phenomena with reference to a Hopf bifurcation subject to white noise and the model of a stochastically driven limit cycle on the cylinder. Furthermore, we investigate the bifurcation behaviour of unbounded noise systems in bounded domains, exhibiting the local character of random bifurcations which are usually hidden in the global analysis.
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SFB-Seminar Berlin
  • 16.01.2018, 14:15 - 15:15
  • 14:15 - 15:15 Quanta of Discrete Spacetime, Alex Goeßmann (TU Berlin)
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  • Space and time - Our daily experience leads to think about those as a continuous manifold. But does this picture remain true, if we look at small length scales inaccessible to our senses? Attempts to unify the fundamental physical descriptions of the world propose that space and time consist of discrete quanta. In the talk, I will present the associated mathematical framework of tensor networks and group fields. Quantum Field Theories of these quanta will be defined and the resulting Feynman diagrams interpreted to carry the geometry of spacetime.
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Job Opening

PostDoc position
  • 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)
  • Dr. hab. Galina Filipuk as Visitor at TU Berlin (18.12.2017 - 19.12.2017)
Forthcoming Guests and Visitors
  • Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
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