• Is it possible to predict the far future before the near future is known accurately? 

      [SNAP-2019-021-EN] Gander, Martin J. (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
      It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict ...
    • Lagrangian mean curvature flow 

      [SNAP-2021-011-EN] Lotay, Jason D. (Mathematisches Forschungsinstitut Oberwolfach, 2021-09-16)
      Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics. I will describe some of the key aspects of Lagrangian mean curvature ...
    • Limits of graph sequences 

      [SNAP-2019-010-EN] Klimošová, Tereza (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent ...
    • The Mathematics of Fluids and Solids 

      [SNAP-2019-019-EN] Kaltenbacher, Barbara; Kukavica, Igor; Lasiecka, Irena; Triggiani, Roberto; Tuffaha, Amjad; Webster, Justin (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-18)
      Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a ...
    • Mixed volumes and mixed integrals 

      [SNAP-2018-014-EN] Rotem, Liran (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-29)
      In recent years, mathematicians have developed new approaches to study convex sets: instead of considering convex sets themselves, they explore certain functions or measures that are related to them. Problems from ...
    • Mixed-dimensional models for real-world applications 

      [SNAP-2019-014-EN] Nordbotten, Jan Martin (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-21)
      We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and ...
    • Nonlinear Acoustics 

      [SNAP-2019-008-EN] Kaltenbacher, Barbara; Brunnhuber, Rainer (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last ...
    • On Logic, Choices and Games 

      [SNAP-2019-009-EN] Oliva, Paulo (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-04)
      Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ...
    • Positive Scalar Curvature and Applications 

      [SNAP-2019-004-ENSNAP-2019-004-ES] Rosenberg, Jonathan; Wraith, David (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-25)
      [also available in Spanish] We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar ...
    • Quantum symmetry 

      [SNAP-2020-005-EN] Weber, Moritz (Mathematisches Forschungsinstitut Oberwolfach, 2020-06-04)
      In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from ...
    • Quantum symmetry 

      [SNAP-2020-009-EN] Caspers, Martijn (Mathematisches Forschungsinstitut Oberwolfach, 2020-12-31)
      The symmetry of objects plays a crucial role in many branches of mathematics and physics. It allowed, for example, the early prediction of the existence of new small particles. “Quantum symmetry” concerns a generalized ...
    • Random matrix theory: Dyson Brownian motion 

      [SNAP-2020-002-EN] Finocchio, Gianluca (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John ...
    • Random permutations 

      [SNAP-2019-007-EN] Betz, Volker (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-12)
      100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult ...
    • Random sampling of domino and lozenge tilings 

      [SNAP-2016-002-EN] Fusy, Éric (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different ...
    • Reflections on hyperbolic space 

      [SNAP-2021-007-EN] Haensch, Anna (Mathematisches Forschungsinstitut Oberwolfach, 2021-08-24)
      In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spaces different from the usual Euclidean space in which this is not true. One of these spaces is the ''hyperbolic space'', ...
    • Rotating needles, vibrating strings, and Fourier summation 

      [SNAP-2020-006-EN] Zahl, Joshua (Mathematisches Forschungsinstitut Oberwolfach, 2020-09-21)
      We give a brief survey of the connection between seemingly unrelated problems such as sets in the plane containing lines pointing in many directions, vibrating strings and drum heads, and a classical problem from Fourier analysis.
    • Searching for structure in complex data: a modern statistical quest 

      [SNAP-2021-003-EN] Loh, Po-Ling (Mathematisches Forschungsinstitut Oberwolfach, 2021-03-29)
      Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must ...
    • Shape space – a paradigm for character animation in computer graphics 

      [SNAP-2020-007-EN] Heeren, Behrend; Rumpf, Martin (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-07)
      Nowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions ...
    • Solving quadratic equations in many variables 

      [SNAP-2017-012-EN] Tignol, Jean-Pierre (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-30)
      Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields have the same properties in relation ...
    • Spaces of Riemannian metrics 

      [SNAP-2017-010-ENSNAP-2017-010-ES] Bustamante, Mauricio; Kordaß, Jan-Bernhard (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-28)
      Riemannian metrics endow smooth manifolds such as surfaces with intrinsic geometric properties, for example with curvature. They also allow us to measure quantities like distances, angles and volumes. These are the ...