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
- 15.11.2016, 14:15 - 16:30
14:15 - 15:15
Salem numbers and discrete groups of automorphisms of algebraic surfaces,
Igor Dolgachev (University of Michigan at Ann Arbor)
- A Salem number is a real algebraic integer greater than one whose all conjugates have absolute value at most one and at least one of them has absolute value one. In particular, a Salem number is a root of a reciprocal monic polynomial with integer coefficients. In complex dynamics the logarithms of Salem numbers are realized as topological entropy of an automorphism of an algebraic surface. In my talk I will explain when such an automorphism exists and which Salem numbers occur in this way.
- 13.12.2016, 14:15 - 16:30
14:15 - 15:15
Richard James (University of Minnesota)
- 10.01.2017, 14:15 - 16:30
During the semester, the SFB TRR109 organizes a colloquium which takes place every four weeks. The organization of the colloquium alternates between the TU Berlin and the TU Munich. The presentations are broadcast live from the hosting university to the partner university.
- Closing Date: 04.11.2016
- Location: TU Berlin
- Type: Ph.D.
- Closing Date: 30.11.2016
- Location: TU München
- Type: Ph.D.
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. Wolfgang K. Schief as Guest Professor at TU Berlin (27.06.2016 - 31.12.2016)
- Prof. Dr. Pavle Blagojević as Guest Professor at FU Berlin (01.07.2016 - 31.12.2016)