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 Technische Universität Berlin as lead university,
- the Technische Universität München as partner university,
- and individual scientists from
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
- 20.04.2018, 10:15 - 11:45
10:15 - 11:45
Magnitude meets persistence. Homology theories for filtered simplicial sets,
Nina Otter (Oxford University, England)
- The Euler characteristic is an invariant of a topological space that in a precise sense captures its canonical notion of size, akin to the cardinality of a set. The Euler characteristic is closely related to the homology of a space, as it can be expressed as the alternating sum of its betti numbers, whenever the sum is well-defined. Thus, one says that homology categorifies the Euler characteristic. In his work on the generalisation of cardinality-like invariants, Leinster introduced the magnitude of a metric space, a real number that gives the “effective number of points” of the space. Recently, Leinster and Shulman introduced a homology theory for metric spaces, called magnitude homology, which categorifies the magnitude of a space. In this talk I will introduce magnitude and magnitude homology, give an answer to these questions and show that they are intertwined: it is the blurred version of magnitude homology that is related to persistent homology.
- 20.04.2018, 12:00 - 13:00
12:00 - 13:00
- 24.04.2018, 14:15 - 15:15
14:15 - 15:15
Decoding of neural data using cohomological learning,
Erik Rybakken (NTNU, Trondheim)
- We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological learning. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus we capture head direction cells and decode the head direction from the neural population activity without having to process the behaviour of the mouse.
- Closing Date: 20.04.2018
- Location: TU Berlin
- Type: Fremdsprachensekretär/in
- Closing Date: 27.04.2018
- Location: TU Berlin
- Type: Geschäftsführer/in
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. Steffen Rohde as Guest Professor at TU Berlin (30.03.2018 - 26.06.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU München (01.04.2018 - 14.06.2018)
- Prof. Dr. Konstantin Mischaikow as Guest Professor at TU München (14.04.2018 - 13.06.2018)
Forthcoming Guests and Visitors
- Associate Prof. Shimpei Kobayashi as Visitor at TU Berlin (15.06.2018 - 14.08.2018)
- Associate Prof. Shimpei Kobayashi as Visitor at TU München (15.08.2018 - 21.09.2018)