• Computing the long term evolution of the solar system with geometric numerical integrators 

      [SNAP-2017-009-EN] Fiorelli Vilmart, Shaula; Vilmart, Gilles (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-27)
      Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the ...
    • Counting self-avoiding walks on the hexagonal lattice 

      [SNAP-2019-006-EN] Duminil-Copin, Hugo (Mathematisches Forschungsinstitut Oberwolfach, 2019-06-04)
      In how many ways can you go for a walk along a lattice grid in such a way that you never meet your own trail? In this snapshot, we describe some combinatorial and statistical aspects of these so-called self-avoiding ...
    • From Betti numbers to ℓ²-Betti numbers 

      [SNAP-2020-001-EN] Kammeyer, Holger; Sauer, Roman (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      We provide a leisurely introduction to ℓ²-Betti numbers, which are topological invariants, by relating them to their much older cousins, Betti numbers. In the end we present an open research problem about ℓ²-Betti numbers.
    • Quantum symmetry 

      [SNAP-2020-005-EN] Weber, Moritz (Mathematisches Forschungsinstitut Oberwolfach, 2020-06-04)
      In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from ...
    • Shape space – a paradigm for character animation in computer graphics 

      [SNAP-2020-007-EN] Heeren, Behrend; Rumpf, Martin (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-07)
      Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ...
    • Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren 

      [SNAP-2021-005-DESNAP-2021-005-EN] Lechner, Gandalf (Mathematisches Forschungsinstitut Oberwolfach, 2021-06-24)
      Die Yang–Baxter-Gleichung ist eine faszinierende Gleichung, die in vielen Gebieten der Physik und der Mathematik auftritt und die am besten diagrammatisch dargestellt wird. Dieser Snapshot schlägt einen weiten Bogen ...