• The adaptive finite element method 

      [SNAP-2016-013-EN] Gallistl, Dietmar (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other ...
    • The Algebraic Statistics of an Oberwolfach Workshop 

      [SNAP-2018-001-EN] Seigal, Anna (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-27)
      Algebraic Statistics builds on the idea that statistical models can be understood via polynomials. Many statistical models are parameterized by polynomials in the model parameters; others are described implicitly by ...
    • Aperiodic Order and Spectral Properties 

      [SNAP-2017-003-EN] Baake, Michael; Damanik, David; Grimm, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)
      Periodic structures like a typical tiled kitchen floor or the arrangement of carbon atoms in a diamond crystal certainly possess a high degree of order. But what is order without periodicity? In this snapshot, we are ...
    • 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.
    • Billiards and flat surfaces 

      [SNAP-2015-001-EN] Davis, Diana (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      [also available in German] Billiards, the study of a ball bouncing around on a table, is a rich area of current mathematical research. We discuss questions and results on billiards, and on the related topic of flat surfaces.
    • 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 ...
    • Closed geodesics on surfaces and Riemannian manifolds 

      [SNAP-2017-005-EN] Radeschi, Marco (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-07)
      Geodesics are special paths in surfaces and so-called Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk ...
    • The codimension 

      [SNAP-2018-009-EN] Lerario, Antonio (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-19)
      In this snapshot we discuss the notion of codimension, which is, in a sense, “dual” to the notion of dimension and is useful when studying the relative position of one object insider another one.
    • Computational Optimal Transport 

      [SNAP-2017-008-EN] Solomon, Justin (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-21)
      Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; ...
    • Computing the long term evolution of the solar system with geometric numerical integrators 

      [SNAP-2017-009-EN] Fiorelli Vilmart, Shaula; Vilmart, Gilles (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-27)
      Simulating the dynamics of the Sun–Earth–Moon system with a standard algorithm yields a dramatically wrong solution, predicting that the Moon is ejected from its orbit. In contrast, a well chosen algorithm with the ...
    • Computing with symmetries 

      [SNAP-2018-003-EN] Roney-Dougal, Colva M. (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-06)
      Group theory is the study of symmetry, and has many applications both within and outside mathematics. In this snapshot, we give a brief introduction to symmetries, and how to compute with them.
    • Curriculum development in university mathematics: where mathematicians and education collide 

      [SNAP-2015-011-EN] Sangwin, Christopher J. (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can ...
    • Darcy's law and groundwater flow modelling 

      [SNAP-2015-007-EN] Schweizer, Ben (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, ...
    • Data assimilation: mathematics for merging models and data 

      [SNAP-2018-011-EN] Morzfeld, Matthias; Reich, Sebastian (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-10)
      When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the ...
    • 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.
    • 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 ...
    • Drugs, herbicides, and numerical simulation 

      [SNAP-2014-010-EN] Benner, Peter; Mena, Hermann; Schneider, René (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      [also available in German] 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 ...
    • Estimating the volume of a convex body 

      [SNAP-2018-015-EN] Baldin, Nicolai (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-30)
      Sometimes the volume of a convex body needs to be estimated, if we cannot calculate it analytically. We explain how statistics can be used not only to approximate the volume of the convex body, but also its shape.
    • Fast Solvers for Highly Oscillatory Problems 

      [SNAP-2018-006-EN] Barnett, Alex (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-26)
      Waves of diverse types surround us. Sound, light and other waves, such as microwaves, are crucial for speech, mobile phones, and other communication technologies. Elastic waves propagating through the Earth bounce ...
    • A few shades of interpolation 

      [SNAP-2017-007-EN] Szpond, Justyna (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-07)
      The topic of this snapshot is interpolation. In the ordinary sense, interpolation means to insert something of a different nature into something else. In mathematics, interpolation means constructing new data points ...