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
Next SFB Workshop
- 04.10. - 06.10.2017
The annual DGD Days on "Discretization in Geometry and Dynamics" will be held this year in the Science and Study Center of the TU München, located in the former Cistercian Monastery of Raitenhaslach in Bayern. The DGD Days program is organized with presentations of key themes in the mornings and with workshops and research exchange groups in the afternoons, providing ample opportunity for discussion and exchange.
- 27.06.2017, 14:15 - 15:15
14:15 - 15:15
Bethe ansatz for Gaudin models,
Evgeny Mukhin (Indiana University-Purdue University Indianapolis)
- Gaudin Hamiltonians are commuting linear operators acting in tensor products of representations of simple Lie algebras. Bethe ansatz is a "physics motivated" method which allows to find eigenvectors and eigenvalues of the Hamiltonians. In this talk I will explain the basics of the gl(n) Bethe ansatz and multiple connections to real and complex algebraic geometry, Fuchsian differential operators, orthogonal polynomials, Selberg type integrals, etc.
15:30 - 16:30
Double Polyhedra – Weaving, knots and helices,
Rinus Roelofs (Hengelo, Netherlands)
- Art can help to like and to understand mathematics.
In 1509 the mathematician Luca Pacioli published his book “La Divina Proportione” in which he introduced the idea of adding a second layer to a polyhedron. With “Elevation” he defined an operation with which the extra skin could be created. About a century later, Kepler showed that we can create polyhedra which have a second skin themselves. With Kepler’s “Stellation” we enter the field of multilayer single-surface structures.
This part of mathematics has attracted many artists, sometimes with the goal of making mathematics visible. Leonarda da Vinci made all the illustrations of Pacioli’s book. But also other artists like Albrecht Dürer, Maurits Cornelis Escher and Kenneth Snelson were inspired by these ideas. Based on their works, I started my own investigations, resulting in new mathematical ideas and new sculptures, which I would like to present.
- 04.07.2017, 14:00 - 15:00
14:00 - 15:00
- 07.07.2017, 14:00 - 15:00
14:00 - 15:00
Ruled surfaces in Plücker geometry,
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 (04.06.2017 - 21.07.2017)
- Prof. Dr. Franz Pedit as Guest Professor at TU Berlin (07.06.2017 - 31.12.2017)
- Rinus Roelofs as Visitor at TU Berlin (24.06.2017 - 28.06.2017)
- Prof. Dr. Martin Schmidt as Visitor at TU Berlin (25.06.2017 - 20.07.2017)
- Prof. Dr. Evgeny Mukhin as Visitor at TU Berlin (25.06.2017 - 30.06.2017)
- Dr. Ross Ogilvie as Visitor at TU Berlin (26.06.2017 - 05.07.2017)
Forthcoming Guests and Visitors
- Prof. Dr. Stephan Tillmann as Guest Professor at TU Berlin (18.07.2017 - 15.01.2018)