• Aperiodic Order and Spectral Properties 

      [SNAP-2017-003-EN] Baake, Michael; Damanik, David; Grimm, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)
      Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are ...
    • Computing with symmetries 

      [SNAP-2018-003-EN] Roney-Dougal, Colva M. (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-06)
      Group theory is the study of symmetry, and has many applications both within and outside mathematics. In this snapshot, we give a brief introduction to symmetries, and how to compute with them.
    • Domino tilings of the Aztec diamond 

      [SNAP-2015-016-EN] Rué, Juanjo (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with ...
    • Footballs and donuts in four dimensions 

      [SNAP-2016-012-EN] Klee, Steven (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world ...
    • Friezes and tilings 

      [SNAP-2015-004-EN] Holm, Thorsten (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such ...
    • How to choose a winner: the mathematics of social choice 

      [SNAP-2015-009-ENSNAP-2015-009-DE] Powers, Victoria Ann (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      [also available in German] Suppose a group of individuals wish to choose among several options, for example electing one of several candidates to a political office or choosing the best contestant in a skating competition. ...
    • 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 ...
    • Random sampling of domino and lozenge tilings 

      [SNAP-2016-002-EN] Fusy, Éric (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different ...
    • 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 ...
    • 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 ...