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Patterns and waves in theory, experiment, and application

Snapshots of modern mathematics from Oberwolfach

Patterns and waves in theory, experiment, and application

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.

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Mathematical subjects

Analysis
Numerics and Scientific Computing

Author(s)

Jason J. Bramburger

License

DOI (Digital Object Identifier)

10.14760/SNAP-2023-001-EN

Download PDF

snapshot-2023-001.pdf

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snapshots: overview

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      Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
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      The periodic tables of algebraic geometry
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      Patterns and waves in theory, experiment, and application
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      Closed geodesics on surfaces
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      Characterizations of intrinsic volumes on convex bodies and convex functions
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      A tale of three curves
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      What is Pattern?
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      Biological Shape Analysis with Geometric Statistics and Learning
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      Representations and degenerations
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      Formation Control and Rigidity Theory
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      Nonlinear Acoustics
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      Random permutations
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      Mixed volumes and mixed integrals
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      Computing with symmetries
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      Topological recursion
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      Solving quadratic equations in many variables
      Chi-Wang Shu
      Mathematics plays a key role in scientific computing
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      Spaces of Riemannian metrics
      Shaula Fiorelli Vilmart, Gilles Vilmart
      Computing the long term evolution of the solar system with geometric numerical integrators
      Justin Solomon
      Computational Optimal Transport
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      A few shades of interpolation
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      Molecular quantum dynamics
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      Closed geodesics on surfaces and Riemannian manifolds
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      Mathematische Modellierung von Krebswachstum
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      Aperiodic Order and Spectral Properties
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      News on quadratic polynomials
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      Jacob Bedrossian
      Towards a Mathematical Theory of Turbulence in Fluids
      Laurent Bartholdi
      Profinite groups
      Dietmar Gallistl
      The adaptive finite element method
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      Footballs and donuts in four dimensions
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      The Willmore Conjecture
      Lior Bary-Soroker
      Prime Tuples in Function Fields
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      Polyhedra and commensurability
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      Symmetry and characters of finite groups
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      Das Problem der Kugelpackung
      Tomasz Szemberg
      On the containment problem
      Éric Fusy
      Random sampling of domino and lozenge tilings
      Magnus Egerstedt
      Swarming robots
      Ulrich Krähmer
      From computer algorithms to quantum field theory: an introduction to operads
      Juanjo Rué
      Domino tilings of the Aztec Diamond
      Sebastian Funk
      The mystery of sleeping sickness – why does it keep waking up?
      Antti Knowles
      Quantum diffusion
      Amanda Swan, Albert Murtha
      Modelling the spread of brain tumours
      J. Marron
      Visual Analysis of Spanish Male Mortality
      Christopher Sangwin
      Curriculum development in university mathematics: where mathematicians and education collide
      Jürg Kramer, Anna-Maria Pippich
      Special values of zeta functions and areas of triangles
      Victoria Powers
      How to choose a winner : the mathematics of social choice
      Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
      Ideas of Newton-Okounkov bodies
      Ben Schweizer
      Darcy’s law and groundwater flow modelling
      Raluca Eftimie
      Modelling communication and movement: from cells to animals and humans
      Tom Solomon
      Chaos and chaotic fluid mixing
      Thorsten Holm
      Friezes and tilings
      George Willis
      Zero-dimensional symmetry
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      Minimizing energy
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      Billiards and flat surfaces
      Peter Benner, Hermann Mena, René Schneider
      Drugs, herbicides, and numerical simulation
      Gregory Knese
      Operator theory and the singular value decomposition
      Alain Valette
      The Kadison-Singer problem
      Ragnar-Olaf Buchweitz, Eleonore Faber
      Swallowtail on the shore
      Howell Tong
      Statistics and dynamical phenomena
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      Arrangements of lines
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      The ternary Goldbach Problem
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      Matrixfaktorisierungen
      John E. McCarthy
      Dirichlet Series

      Mathematical subjects

      Algebra and Number Theory
      Analysis
      Didactics and Education
      Discrete Mathematics and Foundations
      Geometry and Topology
      Numerics and Scientific Computing
      Probability Theory and Statistics

      Connections to other fields

      Chemistry and Earth Science
      Computer Science
      Engineering and Technology
      Finance
      Humanities and Social Sciences
      Life Science
      Physics
      Reflections on Mathematics

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