Recent Submissions

  • Towards a Mathematical Theory of Turbulence in Fluids 

    Bedrossian, Jacob (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery ...
  • Profinite groups 

    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, ...
  • The adaptive finite element method 

    Gallistl, Dietmar (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ...
  • Footballs and donuts in four dimensions 

    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 ...
  • The Willmore Conjecture 

    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.
  • Prime tuples in function fields 

    Bary-Soroker, Lior (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and ...
  • Polyhedra and commensurability 

    Guglielmetti, Rafael; Jacquement, Matthieu (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it ...
  • Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse 

    Deistler, Manfred; Graef, Andreas (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist ...
  • Wie steuert man einen Kran? 

    Altmann, Robert; Heiland, Jan (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Die Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese ...
  • High performance computing on smartphones 

    Patera, Anthony T.; Urban, Karsten (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Nowadays there is a strong demand to simulate even real-world engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a ...
  • Symmetry and characters of finite groups 

    Giannelli, Eugenio; Taylor, Jay (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Over the last two centuries mathematicians have developed an elegant abstract framework to study the natural idea of symmetry. The aim of this snapshot is to gently guide the interested reader through these ideas. In ...
  • Das Problem der Kugelpackung 

    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 ...
  • On the containment problem 

    Szemberg, Tomasz; Szpond, Justyna (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    Mathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called “ideals”. Often there are ...
  • Random sampling of domino and lozenge tilings 

    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 ...
  • Swarming robots 

    Egerstedt, Magnus (Mathematisches Forschungsinstitut Oberwolfach, 2016)
    When lots of robots come together to form shapes, spread in an area, or move in one direction, their motion has to be planned carefully. We discuss how mathematicians devise strategies to help swarms of robots behave like ...