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End date: 2023 × Start date: 2020 × End date: 2014 × Start date: 2010 × Type: Report × Subject: Algebra and Number Theory × WGL Institute: MFO ×

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Now showing 1 - 4 of 4
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    Arrangements of lines
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Harbourne, Brian; Szemberg, Tomasz
    We discuss certain open problems in the context of arrangements of lines in the plane.
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    Swallowtail on the shore
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Buchweitz, Ragnar-Olaf; Faber, Eleonore
    Platonic solids, Felix Klein, H.S.M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not only for their sheer beauty but also because of their many symmetry properties. In this snapshot we will start from these symmetries, move on to groups, singularities, and finally find the connection between a tetrahedron and a “swallowtail”. Our running example is the tetrahedron, but every construction can be carried out with any other of the Platonic solids.
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    The ternary Goldbach problem
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Helfgott, Harald
    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 worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers: "Es scheinet wenigstens, dass eine jede Zahl, die größer ist als 2, ein aggregatum trium numerorum primorum sey. (It seems (...) that every positive integer greater than 2 can be written as the sum of three prime numbers.)" In this snapshot, we will describe to what extent the mathematical community has resolved Goldbach's conjecture, with some emphasis on recent progress.
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    What does ">" really mean?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Reznick, Bruce
    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.