• Das Problem der Kugelpackung 

      [SNAP-2016-004-DE] Dostert, Maria; Krupp, Stefan; Rolfes, Jan Hendrik (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen ...
    • Profinite groups 

      [SNAP-2016-014-EN] Bartholdi, Laurent (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, ...
    • Random permutations 

      [SNAP-2019-007-EN] Betz, Volker (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-12)
      100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult ...
    • Spaces of Riemannian metrics 

      [SNAP-2017-010-EN] Bustamante, Mauricio; Kordaß, Jan-Bernhard (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-28)
      Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the ...
    • Swallowtail on the shore 

      [SNAP-2014-007-EN] Buchweitz, Ragnar-Olaf; Faber, Eleonore (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      Platonic solids, Felix Klein, H.S.M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not ...
    • Topological Complexity, Robotics and Social Choice 

      [SNAP-2018-005-EN] Carrasquel, José; Lupton, Gregory; Oprea, John (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-10)
      Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the ...
    • Topological recursion 

      [SNAP-2018-002-EN] Sułkowski, Piotr (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-05)
      In this snapshot we present the concept of topological recursion – a new, surprisingly powerful formalism at the border of mathematics and physics, which has been actively developed within the last decade. After introducing ...
    • Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives 

      [SNAP-2019-013-EN] Milici, Pietro (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
      When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century ...
    • Tropical geometry 

      [SNAP-2018-007-EN] Brugallé, Erwan; Itenberg, Ilia; Shaw, Kristin; Viro, Oleg (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-19)
      What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical ...
    • Vertex-to-Self Trajectories on the Platonic Solids 

      [SNAP-2020-003-EN] Athreya, Jayadev S.; Aulicino, David (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      We consider the problem of walking in a straight line on the surface of a Platonic solid. While the tetrahedron, octahedron, cube, and icosahedron all exhibit the same behavior, we find a remarkable difference with the ...
    • The Willmore Conjecture 

      [SNAP-2016-011-EN] Nowaczyk, Nikolai (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time.
    • Winkeltreue zahlt sich aus 

      [SNAP-2017-001-DE] Günther, Felix (Mathematisches Forschungsinstitut Oberwolfach, 2017-08-23)
      Nicht nur Seefahrerinnen, auch Computergrafikerinnen und Physikerinnen wissen Winkeltreue zu schätzen. Doch beschränkte Rechenkapazitäten und Vereinfachungen in theoretischen Modellen erfordern es, winkeltreue Abbildungen ...
    • Zero-dimensional symmetry 

      [SNAP-2015-003-EN] Willis, George (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      This snapshot is about zero-dimensional symmetry. Thanks to recent discoveries we now understand such symmetry better than previously imagined possible. While still far from complete, a picture of zero-dimensional symmetry ...