Browsing 2 - Snapshots of Modern Mathematics from Oberwolfach by Issue Date

Now showing items 1-20 of 146

    • Arrangements of lines 

      [SNAP-2014-005-EN] Harbourne, Brian; Szemberg, Tomasz (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      We discuss certain open problems in the context of arrangements of lines in the plane.

    • Operator theory and the singular value decomposition 

      [SNAP-2014-009-EN] Knese, Greg (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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. ...

    • Swallowtail on the shore 

      [SNAP-2014-007-EN] Buchweitz, Ragnar-Olaf; Faber, Eleonore (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 ...

    • Statistics and dynamical phenomena 

      [SNAP-2014-006-EN] Tong, Howell (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 ...

    • 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.

    • Dirichlet Series 

      [SNAP-2014-001-EN] McCarthy, John E. (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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.

    • Matrixfaktorisierungen 

      [SNAP-2014-002-DE] Lerche, Wolfgang (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 ...

    • The Kadison-Singer problem 

      [SNAP-2014-008-EN] Valette, Alain (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 ...

    • Drugs, herbicides, and numerical simulation 

      [SNAP-2014-010-EN] Benner, Peter; Mena, Hermann; Schneider, René (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      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 ...

    • 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 ...

    • Domino tilings of the Aztec diamond 

      [SNAP-2015-016-EN] Rué, Juanjo (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with ...

    • Minimizing energy 

      [SNAP-2015-002-EN] Breiner, Christine (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length? We consider the answer ...

    • Friezes and tilings 

      [SNAP-2015-004-EN] Holm, Thorsten (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such ...

    • Modeling communication and movement: from cells to animals and humans 

      [SNAP-2015-006-EN] Eftimie, Raluca (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species ...

    • Special values of zeta functions and areas of triangles 

      [SNAP-2015-010-EN] Kramer, Jürg; Pippich, Anna-Maria von (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      In this snapshot we give a glimpse of the interplay of special values of zeta functions and volumes of triangles. Special values of zeta functions and their generalizations arise in the computation of volumes of moduli ...

    • Quantum diffusion 

      [SNAP-2015-014-EN] Knowles, Antti (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see ...

    • 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 ...

    • Chaos and chaotic fluid mixing 

      [SNAP-2015-005-EN] Solomon, Tom (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We illustrate this with a single recurrence ...

    • Modelling the spread of brain tumours 

      [SNAP-2015-013-EN] Swan, Amanda; Murtha, Albert (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment ...

    • Ideas of Newton-Okounkov bodies 

      [SNAP-2015-008-EN] Kiritchenko, Valentina; Timorin, Vladlen; Smirnov, Evgeny (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      In this snapshot, we will consider the problem of finding the number of solutions to a given system of polynomial equations. This question leads to the theory of Newton polytopes and Newton-Okounkov bodies of which we will ...