• The ternary Goldbach problem 

      [SNAP-2014-003-ENSNAP-2014-003-DE] Helfgott, Harald (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      [also available in German] Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Ultrafilter methods in combinatorics 

      [SNAP-2021-006-EN] Goldbring, Isaac (Mathematisches Forschungsinstitut Oberwolfach, 2021-06-25)
      Given a set X, ultrafilters determine which subsets of X should be considered as large. We illustrate the use of ultrafilter methods in combinatorics by discussing two cornerstone results in Ramsey theory, namely ...
    • 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 ...
    • Visual analysis of Spanish male mortality 

      [SNAP-2015-012-ENSNAP-2015-012-DE] Marron, J. S. (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      [also available in German] 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 ...
    • What does ">" really mean? 

      [SNAP-2014-004-EN] Reznick, Bruce (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      This Snapshot is about the generalization of ">" from ordinary numbers to so-called fields. At the end, I will touch on some ideas in recent research.
    • 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 ...
    • 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 ...
    • 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 ...