Combinatorial solutions to discrete integrable systems

  • This project is an X-Student Research group, funded by the Berlin University Alliance (BUA). It is now also a MATH+ Student Research group.
  • organized by Niklas Affolter (affolter at, I'm a member of the AG Geometry at TU Berlin.
  • For active participation you can get 6 Credits, no matter the university or the subject you study.
  • Course language is English, but I'm happy to answer German questions as well.
  • We meet weekly 14:15 - 15:45 each Thursday from 20.10.22 - 16.02.23, at MAR 0.015.
  • ISIS course (TU moodle), Vorlesungsverzeichnis, BUA XRSG description

The project

The idea of the X-Research Student Groups and this project in particular is that students do their own research. In this project we look at certain rational recurrence equations on the rectangular lattice. Iterating these equations should lead to very complicated formulas that grow exponentially both in the number of terms and in degree. Instead some magic happens, and the formulas are surprisingly well-behaved. The goal of the project is to write down these formulas explicitly, by (weighted) counting of combinatorial objects associated to some companion graph.

Some reasons why I think this project is suitable for students: Note that as with all research, we cannot know what the precise outcome will be. We will be happy if we find candidate solutions for some of the recursion formulas. Proving the formulas may be something for follow up work, for example in form of a bachelor or master thesis. Depending on the success, there is also the possibility of publishing a joint paper.

Background literature

You do not need to know the contents of the literature listed here, but in case you are wondering where all this is coming from... We are going to consider the equations (Q1) - (Q4), (H1) - (H4), (A1) - (A2) of Previous results for 3-dimensional systems can be found here: Some geometric applications of the previous recurrence:
Supported by the SFB TRR 109 Discretization in Geometry and Dynamics and by MATH+

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