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End date: 2022 × Start date: 2022 × End date: 2014 × Start date: 2010 × Type: Report × WGL Institute: MFO ×

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Now showing 1 - 10 of 10
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    Matrixfaktorisierungen
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Lerche, Wolfgang
    Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden. Wir werden darlegen, warum dieses recht simple Konzept zu erstaunlich tiefen mathematischen Gedankengängen führt und auch in der modernen theoretischen Physik wichtige Anwendungen hat.
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    The Kadison-Singer problem
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Valette, Alain
    In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to determine the basic probabilities associated with a given system. In this snapshot we will present a recent uniqueness result concerning these probabilities.
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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.
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    Dirichlet Series
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) McCarthy, John E.
    Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.
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    Operator theory and the singular value decomposition
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Knese, Greg
    This is a snapshot about operator theory and one of its fundamental tools: the singular value decomposition (SVD). The SVD breaks up linear transformations into simpler mappings, thus unveiling their geometric properties. This tool has become important in many areas of applied mathematics for its ability to organize information. We discuss the SVD in the concrete situation of linear transformations of the plane (such as rotations, reflections, etc.).
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    Drugs, herbicides, and numerical simulation
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Benner, Peter; Mena, Hermann; Schneider, René
    The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon.
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    Statistics and dynamical phenomena
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Tong, Howell
    A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, "What do you do for a living?" He replied, "I model." As my friend is a handsome man, the lady did not question his statement and continued, "What do you model?" "Genes." She then looked at him up and down and said, "Mh, you must be very much in demand." "Yes, very much so, especially after I helped discover a new culprit gene for a common childhood disease." The lady looked puzzled. In this snapshot, I will give you an insight into Statistics, the field that fascinated my friend (and myself) so much. I will concentrate on phenomena that change over time, in other words, dynamical events.