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
  • 19.02.2019, 14:15 - 15:15
  • 14:15 - 15:15 (broadcast to TU Munich) Quad Meshing and Vector Field Design - A Computer Graphics Perspective, Olga Diamanti (TU Berlin)
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  • In the domain of computer graphics, triangle meshes are typically the representation of choice for geometric data - their simplicial nature makes storage, rendering and processing convenient. Even so, quadrilateral meshes are better tailored for other domains - the quad structure allows for alignment to principal curvature directions, which are heavily used to guide computational surface modeling and animation, or for representing directions of stress or strain, commonly considered in architectural design and simulation. As such, automatic and semi-automatic quad mesh generation from triangle meshes remains an active research area in graphics. This talk will outline some of the popular methods in geometry processing for this task, with a particular focus in works involving vector fields that express the modeler's intent of how the quads should be laid out. We will comparatively look at some of the objectives and quality criteria commonly used, among which reliability, robustness, efficiency and expressiveness, and state some of the remaining open problems.
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Kis-Sem: Keep it simple Seminar
  • 22.02.2019, 12:00 - 13:00
  • 12:00 - 13:00 TBA, Niklas Affolter 
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SFB-Seminar Berlin
  • 26.02.2019, 14:15 - 15:15
  • 14:15 - 15:15 Leave, flowers, and sea-slugs: From discrete geometry to discrete mechanics, Shankar Venkataramani (The University of Arizona)
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  • I will talk about some geometric questions that arise in the study of soft/thin objects with negative curvature. After reviewing basic ideas from the mechanics of Non-Euclidean sheets, I will discuss the role of non-smooth isometries in explaining the observed morphologies of thin Non-Euclidean sheets. I will highlight the role of DDG methods in constructing the relevant non-smooth solutions and discuss potential extensions of DDG ideas in order to make the jump from solving for isometries to solving for the mechanical equilibrium, i.e force, and moment balance.
    This is joint work with Toby Shearman and Ken Yamamoto.
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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. 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)
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