• Algebra, matrices, and computers 

      [SNAP-2019-005-EN] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-03)
      What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that ...
    • Configuration spaces and braid groups 

      [SNAP-2019-011-EN] Jiménez Rolland, Rita; Xicoténcatl, Miguel A. (Mathematisches Forschungsinstitut Oberwolfach, 2019-10-08)
      In this snapshot we introduce configuration spaces and explain how a mathematician studies their ‘shape’. This will lead us to consider paths of configurations and braid groups, and to explore how algebraic properties of ...
    • Counting self-avoiding walks on the hexagonal lattice 

      [SNAP-2019-006-EN] Duminil-Copin, Hugo (Mathematisches Forschungsinstitut Oberwolfach, 2019-06-04)
      In how many ways can you go for a walk along a lattice grid in such a way that you never meet your own trail? In this snapshot, we describe some combinatorial and statistical aspects of these so-called self-avoiding ...
    • Diophantine equations and why they are hard 

      [SNAP-2019-003-EN] Pasten, Hector (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-24)
      Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. ...
    • 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 ...
    • 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 ...
    • On radial basis functions 

      [SNAP-2019-002-EN] Buhmann, Martin; Jäger, Janin (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-13)
      Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ...
    • Positive Scalar Curvature and Applications 

      [SNAP-2019-004-EN] Rosenberg, Jonathan; Wraith, David (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-25)
      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 curvature. We discuss ...
    • 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 ...
    • Snake graphs, perfect matchings and continued fractions 

      [SNAP-2019-001-EN] Schiffler, Ralf (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13)
      A continued fraction is a way of representing a real number by a sequence of integers. We present a new way to think about these continued fractions using snake graphs, which are sequences of squares in the plane. You ...