• 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 ...
    • A tale of three curves 

      [SNAP-2022-010-EN] Balakrishnan, Jennifer S. (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-27)
      In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th ...
    • The ternary Goldbach problem 

      [SNAP-2014-003-EN] Helfgott, Harald (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 and polymath who lived and ...
    • Das ternäre Goldbach-Problem 

      [SNAP-2014-003-DE] Helfgott, Harald (Mathematisches Forschungsinstitut Oberwolfach, 2020)
      Leonhard Euler (1707–1783) war einer der besten Mathematiker des 18. Jahrhunderts und wohl auch aller Zeiten. Er korrespondierte oft mit seinem Freund, Christoph Goldbach (1690–1764), einem Universalgelehrten, der auch ...
    • 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-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 ...
    • Eine visuelle Analyse der Sterblichkeit männlicher Spanier 

      [SNAP-2015-012-DE] Marron, J. S. (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      Die statistische Visualisierung benutzt graphische Methoden um Erkenntnisse aus Daten zu gewinnen. Wir zeigen wie mit dem Verfahren der Hauptkomponentenanalyse die Sterblichkeit in Spanien im Laufe der letzten hundert Jahre ...
    • 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.
    • What is pattern? 

      [SNAP-2022-009-EN] Baake, Michael; Grimm, Uwe; Moody, Robert V. (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
      Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.
    • Wie man einen Sieger wählt: die Mathematik der Sozialwahl 

      [SNAP-2015-009-DE] Powers, Victoria Ann (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      Angenommen, eine Gruppe von Einzelpersonen möchte unter verschiedenen Optionen wählen, zum Beispiel einen von mehreren Kandidaten für ein politisches Amt oder den besten Teilnehmer einer Eiskunstlaufmeisterschaft. Man ...
    • 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 ...