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 SFB Workshop

Research in Groups 2016
  • 17.12. - 22.12.2016
  • The workshop will offer a unique opportunity for intensive scientific exchange between researchers of the cooperative projects and guests of the SFB TRR109 „Discretization in Geometry and Dynamics“. The goal is to press ahead research of SFB groups from the various institutions and to finalize joint publications of researchers from different projects and places.
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Next Seminars

SFB Colloquium
  • 13.12.2016, 14:15 - 15:15
  • 14:15 - 15:15 (@TUM) Atomistically inspired origami, Richard D. James (University of Minnesota)
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  • “Objective Structures” are structures generated as orbits of discrete groups of isometries. We comment on their unexpected prevalence in nanoscience, materials science and biology and also explain why they arise in a natural way as distinguished structures in quantum mechanics, molecular dynamics and continuum mechanics. The underlying mathematical idea is that the isometry group that generates the structure matches the invariance group of the differential equations. Their characteristic features in molecular science imply highly desirable features for macroscopic structures, particularly 4D structures that deform. We illustrate the latter by constructing some “objective origami” structures.
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SFB Colloquium
  • 10.01.2017, 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.
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SFB Colloquium
  • 07.02.2017, 14:15 - 16:30
  • 14:15 - 15:15 (@tTUM) tba, Axel Voigt (TU Dresden)
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  • 15:30 - 16:30 (@TUM) tba, Fred Chazal (INRIA France)
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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. Wolfgang K. Schief as Guest Professor at TU Berlin (27.06.2016 - 20.02.2017)
  • Prof. Dr. Pavle Blagojević as Guest Professor at FU Berlin (01.07.2016 - 31.12.2016)
Forthcoming Guests and Visitors
  • Prof. Dr. Peter Schröder as Visitor at TU Berlin (08.12.2016 - 22.12.2016)
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