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
- 21.11.2017, 14:15 - 16:30
14:15 - 15:15
Complexity of 3-Manifolds,
Stephan Tillmann (The University of Sydney)
- The complexity of a 3-manifold is the minimum number of tetrahedra in a triangulation of the manifold. It was defined and first studied by Matveev in 1990. The complexity is generally difficult to compute, and various upper and lower bounds have been derived during the last decade using fundamental group, homology or hyperbolic volume.
Effective bounds have only been found in joint work with Jaco, Rubinstein and, more recently, Spreer. Our bounds not only allowed us to determine the first infinite classes of minimal triangulations of closed 3-manifolds, but they also lead to a structure theory of minimal triangulations.
In this talk, I will give a general introduction to complexity of 3-manifolds and explain its ramifications for algorithmic problems in the study of 3-manifolds.
15:30 - 16:30
The story of infinitesimals: a conspiracy of silence ?,
Daryl Cooper (University of California at Santa Barbara)
- The hyperreals are an ordered field containing the real numbers as well as infinitesimals and infinitely large numbers. In some sense they have ALL the properties of the real numbers. They have languished for 60 years, spurned by most professionals. The situation recalls the slow acceptance of other extensions of the concept of number. I will construct the hyperreals, and say a few words about doing geometry and topology with these guys.
- 24.11.2017, 12:00 - 13:00
12:00 - 13:00
- 28.11.2017, 14:00 - 15:00
14:00 - 15:00
- Closing Date: 11.12.2017
- Location: TU München
- Type: Ph.D.
- Closing Date: 31.12.2017
- Location: TU Graz
- Type: PostDoc
Current Guests and Visitors
- Prof. Dr. Bernd Sturmfels as Einstein Visiting Fellow at TU Berlin (01.05.2015 - 30.04.2018)
- Prof. Dr. Francisco Santos as Einstein Visiting Fellow at FU Berlin (01.04.2016 - 31.03.2019)
- Prof. Dr. Franz Pedit as Guest Professor at TU Berlin (07.06.2017 - 31.12.2017)
- Prof. Dr. Stephan Tillmann as Guest Professor at TU Berlin (18.07.2017 - 15.01.2018)
- Tetsuya Nakamura as Visitor at TU Berlin (04.09.2017 - 12.01.2018)
Forthcoming Guests and Visitors
- Prof. Dr. Serguei Agafonov as Visitor at TU Berlin (22.11.2017 - 23.12.2017)
- Prof. Dr. Wolfgang K. Schief as Guest Professor at TU Berlin (26.11.2017 - 20.02.2018)
- Prof. Edmund O. Harris as Visitor at TU Berlin (04.12.2017 - 06.12.2017)
- Prof. Dr. Peter Schröder as Guest Professor at TU Berlin (09.12.2017 - 19.12.2017)
- Dr. hab. Galina Filipuk as Visitor at TU Berlin (18.12.2017 - 19.12.2017)