Discretization in Geometry and Dynamics
SFB Transregio 109

The Collaborative Research Center (SFB TRR) 109 reseraches the discretization of geometric structures and dynamic processes. That means, that they dismantle smooth geometric objects, such as curved surfaces, into simple basic elements, or reduce continual processes, such as the flight paths of satellites, into their partial steps.

 

Collaborative Project: Discretization in Geometry and Dynamics (DGD)

This transregional research project is financed by the German Reserach Foundation (DFG) and is headed by the TU Berlin with the TUM as the partner university. Leading scientists from the FU Berlin, TU Graz, TU Wien and IST Austria complete the group. In a total of 17 projects, 120 mathematicians work on questions concerning the discretization of geometric structures and dynamic processes as well as in the area of computation.

Discretization enables the calculation and analsysis on computers and is used in areas such as computer graphics, digital signal processing and numerical simulations.

Contact

Diane Clayton-Winter

Diane Clayton-Winter

Team Assistant

M10, Zentrum Mathematik

Boltzmannstr. 3
85748 Garching b. München

Tel.: +49 (0)89 289 18352

 clayton (at) ma.tum.de

Mathematical methods as technology of the future

Modell: Geschwungenes Glasdach aus geometrischen Formen

„Bisherige Methoden ermöglichen nur Näherungswerte, die für viele Aufgaben heute nicht mehr ausreichen“, erläutert der Sprecher Alexander Bobenko, Professor für Geometrie an der TU Berlin. „Um bessere Ergebnisse zu erzielen, wollen wir daher sogenannte strukturbewahrende Diskretisierungen finden, untersuchen und anwenden. Man könnte auch sagen, wir wollen nicht mehr nur einzelne Gleichungen, sondern gleich die zugrundliegenden Theorien diskretisieren“.

Konkret untersuchen die Forscher Diskretisierungen, für die es in wichtigen Aspekten keine strukturellen Unterschiede zu entsprechenden glatten Flächen oder kontinuierlichen dynamischen Prozessen gibt. So beschäftigt sich etwa ein Teilprojekt mit der Zerlegung geschwungener Oberflächen in ebene Vierecke. Damit lässt sich ein geschwungenen Glasdach konstruieren - mit einfach zu fertigenden Bauelementen. Dies ermöglicht es, eine kostengünstige und ästhetisch ansprechende architektonische Idee zu realisieren.

DFG funds a second research period of the SFB TRR 109

In 2012 the Technical University of Munich received, together with the Technical University of Berlin, an award of six milion Euros for the first four years of the mathematical research project SFB/TRR109. From 2016 the DFG supports the SFB/TRR109 for a further four years to the sum of 7 million Euros.

„The continuation of the Collaborative Research Center illustrates the excellent cooperation within our group over the past four years. The extension of the scope of the project is a clear sign for the future of our group, " said the speaker of the group Alexander Bobenko, Professor for Geometry at the TU Berlin on recieving the good news.

 „This further support of our work makes is possible for us to deepen our research in this interesting and challenging area of mathematics. We can be proud of this result," added deputy speaker Folkmar Bornemann, Professor for Scientific Computing at the TUM.

The Collaborative Research Center brings together scientists from the TU Berlin (as lead university) and the TUM as partner university with colleagues from the FU Berlin, the TU Graz, the IST Austria and the TU Vienna. In a total of 17 projects more than 120 mathematicians are working on problems in the areas of discretization of geometric structures and dynamic processes. The area "computation" has been significantly extended in the new research period, with a total of seven subprojects, aiming to keep abreast of current developments. 

The area of public relations also receives more support, particularly in the areas of computer-aided media and film. The support of young researches remains a central objective of the research work, with numerous research jobs for doctorate and postdoctorate students financed by the DFG. 

SFB Publications from TUM scientists

A. Montag, J. Richter-Gebert, Z02

CindyGL: Authoring GPU-Based Interactive Mathematical Content 
Mathematical Software – ICMS 2016, Volume 9725 of the series Lecture Notes in Computer Science pp 359-365 
2016 
Link 

 

M. von Gagern, J. Richter-Gebert, Z02

CindyJS Plugins: Extending the Mathematical Visualization Framework 
Mathematical Software – ICMS 2016, Volume 9725 of the series Lecture Notes in Computer Science pp 327-334 
2016 
Link 

 

M. von Gagern, U. Kortenkamp, J. Richter-Gebert, M. Strobel, Z02

CindyJS: Mathematical Visualization on Modern Devices 
Mathematical Software – ICMS 2016, Volume 9725 of the series Lecture Notes in Computer Science pp 319-326 
2016 
Link 

 

Bornemann, F. and Its, A. and Olver, S. and Wechslberger, G., B03

Numerical Methods for the Discrete Map Za 
In Collection: Advances in Discrete Differential Geometry, Springer 
2016
Download 

 

Bücking, U. and Matthes, D., B09

Constructing solutions to the Björling problem for isothermic surfaces by structure preserving discretization 
In Collection: Advances in Discrete Differential Geometry, Springer 
2016
Download 

 

Bobenko, A. I. and Hoffmann, T., A02

S-conical cmc surfaces. Towards a unified theory of discrete surfaces with constant mean curvature 
In Collection: Advances in Discrete Differential Geometry, Springer 
2016 
Download

Mennemann, J-F and Matthes, D and Weishäupl, R-M and Langen, T

Optimal control of Bose-Einstein condensates in three dimensions 
Journal: New Journal of Physics, 17(11):113027 
Nov 2015
Download 

 

Johannes Keller, B06

Quantum Dynamics on Potential Energy Surfaces-Simpler States and Simpler Dynamics 
Dissertation: October 2015 

 

Hoffmann, T. and Sageman-Furnas, A. O., A02

A 2x2 Lax representation, associated family, and Bäcklund transformation for circular K-nets 
Oct 2015
Download 

 

Kranich, Stefan, B01

Generation of real algebraic loci via complex detours 
preprint, Oct 2015
Download 

 

Bornemann, Folkmar and Forrester, Peter J., B03

Singular values and evenness symmetry in random matrix theory 
Journal: Forum Math. (ahead of print); 19pp 
Oct 2015
DOI: 10.1515/forum-2015-0055 

Download 

 

Horst Osberger, B09

Fully variational Lagrangian discretizations for second and fourth order evolution equations 
Dissertation: September 2015

 

Georg Wechslberger, B03

Automatic Contour Deformation of Riemann-Hilbert Problems 
Dissertation: July 2015
Download

 

Stefan Kranich, B01

GPU-based visualization of domain-coloured algebraic Riemann surfaces. 
Preprint, July 2015
Download 

 

Folkmar Bornemann, Michael La Croix, B03

The singular values of the GOE
Random Matrices: Theory Appl. 04, 1550009 (2015) (32 pages) 
June 2015.
Download
External 

 

Stefan Kranich, B01

An epsilon-delta bound for plane algebraic curves and its use for certified homotopy continuation of systems of plane algebraic curves. 
Preprint, May 2015
Download 

 

Folkmar Bornemann, B03

A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge 
3pp, e-print, 2015
Download 

 

Folkmar Bornemann, Peter J. Forrester, B03

Singular values and evenness symmetry in random matrix theory 
21pp, e-print, 2015
Download 

 

Horst Osberger, Daniel Matthes, B09

Convergence of a Fully Discrete Variational Scheme for a Thin Film Equation. 
Submitted to Radon Series on Computational and Applied Mathematics, 2015 

 

Horst Osberger, B09

Long-Time Behaviour of a Fully Discrete {Lagrangian} Scheme for a Family of Fourth Order
Submitted, 2015
Download  

 

Jonathan Zinsl, Daniel Matthes, B09

Transport Distances and Geodesic Convexity for Systems of Degenerate Diffusion Equations
In revision at Calculus of Variations and Partial Differential Equations, 2015
Download  

 

Daniel Matthes, Jan Maas, B09

Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation. 
submitted, 2015 
Download 

 

Jonathan Zinsl, Daniel Matthes, B09

Exponential Convergence to Equilibrium in a Coupled Gradient Flow System Modelling Chemotaxis
Analysis \& PDE, vol. 8, nr. 2, pp.425-466, 2015
Arxiv Download  

 

Benedict Dingfelder, J.A.C. Weidemann, B03

An improved Talbot method for numerical Laplace transform inversion.
Numer. Algorithms 68, pp. 167-183, 2015 
External  

Daniel Matthes, Horst Osberger, B09

Convergence of a Variational Lagrangian Scheme for a Nonlinear Drift Diffusion Equation. 
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 43, Nr. 3, pp.697-726. 
Cambridge Univ. Press, 2014 
Download 

 

Daniel Matthes, Horst Osberger, B09

A Convergent {Lagrangian} Discretization for a Nonlinear Fourth Order Equation. 
submitted, 2014 
Download 

 

Jonathan Zinsl, B09

Geodesically Convex Energies and Confinement of Solutions for a Multi-Component System of Nonlocal Interaction Equations
submitted, 2014
Download  

 

Ciprian S. Borcea and Ileana Streinu, Gastprofessorin C01

Liftings and stresses for planar periodic frameworks 
in Proc. 30th Symposium on Computational Geometry (SoCG'14), 2014.
Download

 

Ciprian S. Borcea and Ileana Streinu, Gastprofessorin C01

Kinematics of Expansive Planar Periodic Mechanisms 
Advances in Robot Kinematics (ARK'14), 2014.
Download

Yuen Au Yeung, B08

Crystalline Order, Surface Energy Densities and Wulff Shapes: Emergence from Atomistic Models 
PHD Thesis, 2013
Download

 

C. Lasser, S. Troppmann, B06

Hagedorn wavepackets in time-frequency and phase space 
e-print 2013
Download 

 

N.S. Witte, F. Bornemann, P.J.Forrester, B03

Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles. 
Nonlinearity 26, pp. 1799-1822
2013.
Download 

 

Georg Wechslberger, Folkmar Bornemann, B03

Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlevé II Transcendents.
Constr. Approx. 2014 (published online June 2013), 21pp
Download  

 

Johannes Keller, Caroline Lasser, B06

Propagation of Quantum Expectations with Husimi Functions.
To appear in SIAM J. Appl. Math. 
Juni 2013.
Download  

J. Richter-Gebert, C01 und U. Kortenkamp

The Cinderella.2 Manual: Working with The Interactive Geometry Software 
2012 

Alle Publikationen des SFB TRR 109 finden Sie hier in den Listen.