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
  • 10.12.2018, 14:15 - 15:15
  • 14:15 - 15:15 (Monday!) TBA, Barbara Zwicknagl (TU Berlin)
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SFB Colloquium
  • 11.12.2018, 14:15 - 16:30
  • 14:15 - 15:15 (@TUM) Approximate curvatures of a varifold, Gian Paolo Leonardi (University of Modena and Reggio Emilia)
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  • Varifolds, i.e. Radon measures on the Grassmannian bundle of unoriented tangent d-planes of a Riemannian n-manifold M, represent a variational generalization of unoriented, d-dimensional submanifolds of M. By a suitable extension of classical variation operators, we introduce a notion of approximate second fundamental form that is well-defined for a generic varifold. Rectifiability, compactness, and convergence results are proved, showing in particular the consistency and stability of approximate curvatures with respect to varifold convergence. If restricted to the case of "discrete varifolds", this theory provides a general framework for extracting key features from discrete geometric data. Some numerical tests on point clouds (evaluation of curvatures and geometric flows, also in presence of noise and singularities) will be shown. We shall finally discuss some future perspectives and open problems. This is a joint research with Blanche Buet (Univ. Paris XI - Orsay) and Simon Masnou (Univ. Lyon 1).
  • 15:30 - 16:30 (@TUM) A review on some mathematical results about crystallization, Xavier Blanc (Université Paris-Diderot)
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  • In this talk, I will review some results on the crystallization conjecture, that is, the mathematical proof of the fact that, under appropriate conditions, interacting particles place themselves into periodic configurations. I will first review classical models at zero temperature, in which few results have been proved. Apart from the question of the emergence of periodicity, determination of the optimal lattice, in link with special functions, will be addressed. Then, some problems regarding the quantum case, in which the notion of crystalline order needs to be defined in a different way. Similarities with positive temperature classical models will be outlined. This is a joint work with M. Lewin (Univ. Paris Dauphine)
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SFB-Seminar Berlin
  • 18.12.2018, 14:15 - 15:15
  • 14:15 - 15:15 TBA, Niklas Affolter (TU Berlin)
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Job Opening

Fremdsprachensekretär/in
  • Closing Date: 14.12.2018
  • Location: TU Berlin
  • Type: Fremdsprachensekretär/in
Current Guests and Visitors
  • Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 31.07.2020)
  • Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2016 - 31.03.2019)
  • Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
  • Prof. Dr. Dierk Schleicher as Guest Professor at TU Berlin (01.11.2018 - 31.12.2018)
  • Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (17.11.2018 - 12.02.2019)
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