Snapshots of Modern Mathematics from Oberwolfach

Permanent URI for this collection

https://oa.tib.eu/renate/handle/123456789/14628

Browse

Recent Submissions

Now showing 1 - 5 of 134
  • Thumbnail Image
    Item
    Closed geodesics on surfaces
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Dozier, Benjamin
    We consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces.
  • Thumbnail Image
    Item
    Patterns and Waves in Theory, Experiment, and Application
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2023) Bramburger, Jason J.
    In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social processes. We begin by focussing on two types of patterns that do not change in time: space-filling patterns and localized patterns. We then discuss two types of waves that evolve predictably as time goes on: spreading waves and rotating waves. All our examples are motivated with real-world applications and we highlight some of the main lines of research that mathematicians pursue to better understand them.
  • Thumbnail Image
    Item
    What is pattern?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Baake, Michael; Grimm, Uwe; Moody, Robert V.
    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.
  • Thumbnail Image
    Item
    Characterizations of intrinsic volumes on convex bodies and convex functions
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Mussnig, Fabian
    If we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of classical mathematical results. We also take a look at applications and new generalizations to the setting of functions.
  • Thumbnail Image
    Item
    A tale of three curves
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Balakrishnan, Jennifer S.
    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 century. To answer these questions, we describe a selection of techniques in modern number theory that can be used to determine the set of rational points on a curve.