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
  • 27.11.2018, 13:00 - 13:45
  • 13:00 - 13:45 (Exceptional time and room MA 313!!!) Structure and Randomness in Signal Processing, Felix Krahmer (TU München)
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  • In this talk, we will discuss various examples how mathematically inspired measurement design in signal processing applications yields improved performance and allows for provable error guarantees, crucial for critical applications. Firstly, motivated by computational imaging applications, we discuss the problem of sparse recovery from subsampled random convolutions. We advance techniques related to the theory of empirical processes to establish near-optimal recovery guarantees.
    Secondly, we introduce a mathematical theory that complements recent analog-to-digital converter designs to allow for the reconstruction of bandlimited signals even when the dynamic range is limited. Our results are driven by the need for cheap quantizers to design low-cost sensors and cameras.
    Lastly, motivated by applications in wireless communication, we consider the problem of simultaneous blind demixing and deconvolution for randomly encoded signals, as it arises in the context of sporadic non-coherent multi-user communication. Our results establish for the first time near-optimal parameter dependence.
    These are joint works with the speaker’s PhD student Dominik Stöger, as well as with Shahar Mendelson (Technion), Holger Rauhut (RWTH Aachen), Peter Jung (TU Berlin/HHI), Ayush Bhandari (MIT), and Ramesh Raskar (MIT).
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SFB Colloquium
  • 27.11.2018, 14:15 - 16:30
  • 14:15 - 15:15 (@TUB) TBA, Dierk Schleicher (Jakobs University Bremen)
  • more
Kis-Sem: Keep it simple Seminar
  • 30.11.2018, 12:00 - 13:00
  • 12:00 - 13:00 TBA, Marcel Padilla 
  • more
Job Opening

SHK 40-80 St/Monat
  • Closing Date: 30.11.2018
  • Location: TU Berlin
  • Type: Studentische Hilfskraft
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. Wolfgang K. Schief as Guest Professor at TU Berlin (17.11.2018 - 12.02.2019)
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