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
- 22.05.2018, 14:15 - 15:15
14:15 - 15:15
Discrete Gaussian distributions via theta functions,
Daniele Agostini (MPI MIS Leipzig)
- Maximum entropy probability distributions are important for information theory and relate directly to exponential families in statistics. Having the property of maximizing entropy can be used to define a discrete analogue of the classical continuous Gaussian distribution. We present a parametrization of such a density using the Riemann Theta function, use it to derive fundamental properties and exhibit strong connections to the study of abelian varieties in algebraic geometry. This is joint work with Carlos Améndola (TU Munich).
- 01.06.2018, 12:00 - 13:00
12:00 - 13:00
- 12.06.2018, 14:15 - 16:30
14:15 - 15:15
Steffen Rohde (University of Washington & DGD Guest Professor)
15:30 - 16:30
Optimizing over convex functions: motivations and challenges,
Guillaume Carlier (Université Paris Dauphine & John von Neumann Professor@TUM)
- Optimization problems subject to a convexity constraint on the admissible profiles arise in a variety of contexts in aerodynamics, economics, geometry, shape optimization, mass transport.... They are challenging because discretizing convex functions or shapes is in general very costly and naive algorithms maybe inconsistent. In this survey talk, after describing some applications and theoretical results I will review some tractable numerical approaches to these problems.
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)