• Emergence in biology and social sciences 

      [SNAP-2022-001-EN] Hoffmann, Franca; Merino-Aceituno, Sara (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-31)
      Mathematics is the key to linking scientific knowledge at different scales: from microscopic to macroscopic dynamics. This link gives us understanding on the emergence of observable patterns like flocking of birds, leaf ...
    • Searching for the monster in the trees 

      [SNAP-2022-003-EN] Craven, David A. (Mathematisches Forschungsinstitut Oberwolfach, 2022-04-13)
      The Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite ...
    • Seeing through rock with help from optimal transport 

      [SNAP-2022-004-EN] Frederick, Christina; Yang, Yunan (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-06)
      Geophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the ...
    • The Robinson–Schensted algorithm 

      [SNAP-2022-002-EN] Thomas, Hugh (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-06)
      I am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a ...
    • Jewellery from tessellations of hyperbolic space 

      [SNAP-2022-005-EN] Gangl, Herbert (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-02)
      In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional ...
    • Solving inverse problems with Bayes' theorem 

      [SNAP-2022-006-EN] Latz, Jonas; Sprungk, Björn (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-05)
      The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as ...
    • What is pattern? 

      [SNAP-2022-009-EN] Baake, Michael; Grimm, Uwe; Moody, Robert V. (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
      Pattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics.
    • Representations and degenerations 

      [SNAP-2022-007-EN] Dumanski, Ilya; Kiritchenko, Valentina (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
      In this snapshot, we explain two important mathematical concepts (representation and degeneration) in elementary terms. We will focus on the simplest meaningful examples, and motivate both concepts by study of symmetry.
    • Biological shape analysis with geometric statistics and learning 

      [SNAP-2022-008-EN] Utpala, Saiteja; Miolane, Nina (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-25)
      The advances in biomedical imaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, shape data may hold ...
    • A tale of three curves 

      [SNAP-2022-010-EN] Balakrishnan, Jennifer S. (Mathematisches Forschungsinstitut Oberwolfach, 2022-10-27)
      In this snapshot, we give a survey of some problems in the study of rational points on higher genus curves, discussing questions ranging from the era of the ancient Greeks to a few posed by mathematicians of the 20th ...