Discretization in Geometry and Dynamics
SFB Transregio 109

 

Registration for DGD Days open till 12.07.2019

DGD Days 2019 registration

 

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.
 

Film featuring the work of the SFB

"The Discrete Charm of Geometry"
 

Next Seminars

SFB-Seminar Berlin
  • 18.10.2019, 10:30 - 11:30
  • 10:30 - 11:30 (@TUB) Circle packings and Delaunay circle patterns on surfaces with complex projective structures, Jean-Marc Schlenker (University of Luxembourg)
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  • We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending a complex projective structure admitting a circle packing with given nerve (resp. a Delaunay circle pattern with given nerve and intersection angles) to the underlying complex structure is proper. The talk will contain an introduction to complex projective structures on surfaces. Joint with Andrew Yarmola (Princeton University).
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SFB Colloquium
  • 05.11.2019, 14:15 - 16:30
  • 14:15 - 15:15 (@TUM) Semi-discrete unbalanced optimal transport and quantization, Bernhard Schmitzer (TUM)
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  • Semi-discrete optimal transport between a discrete source and a continuous target has intriguing geometric properties and applications in modelling and numerical methods. Unbalanced transport, which allows the comparison of measures with unequal mass, has recently been studied in great detail by various authors. In this talk we consider the combination of both concepts. The tessellation structure of semi-discrete transport survives and there is an interplay between the length scales of the discrete source and unbalanced transport which leads to qualitatively new regimes in the crystallization limit. Based on joint work with David P. Bourne and Benedikt Wirth.
  • 15:30 - 16:30 (@TUM) tba, Facundo Memoli (Ohio State University)
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SFB Colloquium
  • 03.12.2019, 14:15 - 16:30
  • 14:15 - 15:15 (@ TUM) tba, Heather Harrington (University of Oxford)
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  • 15:30 - 16:30 (@TUM) tba, David Bourne (Heriot-Watt University, Edinburgh)
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Current Guests and Visitors
  • Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 31.07.2020)
  • Prof. Dr. Peter Schröder as Einstein Visiting Fellow at TU Berlin (01.03.2018 - 28.02.2021)
  • Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2019 - 31.03.2021)
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