• Darcy's law and groundwater flow modelling 

      [SNAP-2015-007-EN] Schweizer, Ben (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ...
    • The mystery of sleeping sickness – why does it keep waking up? 

      [SNAP-2015-015-EN] Funk, Sebastian (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about ...
    • Curriculum development in university mathematics: where mathematicians and education collide 

      [SNAP-2015-011-EN] Sangwin, Christopher J. (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can ...
    • From computer algorithms to quantum field theory: an introduction to operads 

      [SNAP-2015-017-EN] Krähmer, Ulrich (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and ...
    • Billard und ebene Flächen 

      [SNAP-2015-001-DE] Davis, Diana (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Billard, die Zick-Zack-Bewegungen eines Balls auf einem Tisch, ist ein reichhaltiges Feld gegenwärtiger mathematischer Forschung. In diesem Artikel diskutieren wir Fragen und Antworten zum Thema Billard, und zu dem damit ...
    • How to choose a winner: the mathematics of social choice 

      [SNAP-2015-009-EN] Powers, Victoria Ann (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      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. The group might ask: what ...
    • Visual analysis of Spanish male mortality 

      [SNAP-2015-012-EN] Marron, J. S. (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Statistical visualization uses graphical methods to gain insights from data. Here we show how a technique called principal component analysis is used to analyze mortality in Spain over about the last hundred years. This ...
    • Billiards and flat surfaces 

      [SNAP-2015-001-EN] Davis, Diana (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Billiards, the study of a ball bouncing around on a table, is a rich area of current mathematical research. We discuss questions and results on billiards, and on the related topic of flat surfaces.
    • Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse 

      [SNAP-2016-008-DE] 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 ...
    • The adaptive finite element method 

      [SNAP-2016-013-EN] 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 ...
    • Prime tuples in function fields 

      [SNAP-2016-010-EN] 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 ...
    • 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 ...
    • Towards a Mathematical Theory of Turbulence in Fluids 

      [SNAP-2016-015-EN] 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 ...
    • Swarming robots 

      [SNAP-2016-001-EN] 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 ...
    • Wie steuert man einen Kran? 

      [SNAP-2016-007-DE] 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 ...
    • Symmetry and characters of finite groups 

      [SNAP-2016-005-EN] 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 ...
    • 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, ...
    • On the containment problem 

      [SNAP-2016-003-EN] 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 ...
    • High performance computing on smartphones 

      [SNAP-2016-006-EN] 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 ...
    • 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 ...