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Patterns and waves in theory, experiment, and application

Schnappschüsse moderner Mathematik aus 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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Mathematisches Fachgebiet

Analysis
Numerik und Wissenschaftliches Rechnen

Autor(en)

Jason J. Bramburger

Lizenz

DOI (Digital Object Identifier)

10.14760/SNAP-2023-001-EN

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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
      Kathrin Hellmuth, Christian Klingenberg
      Route planning for bacteria
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      Characterizations of intrinsic volumes on convex bodies and convex functions
      Jennifer S. Balakrishnan
      A tale of three curves
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      What is Pattern?
      Saiteja Utpala, Nina Miolane
      Biological Shape Analysis with Geometric Statistics and Learning
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      Representations and degenerations
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      Solving inverse problems with Bayes’ theorem
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      Jewellery from tessellations of hyperbolic space
      Chr istina Frederick, Yunan Yang
      Seeing through rock with help from optimal transport
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      Searching for the Monster in the Trees
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      The Robinson–Schensted algorithm
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      Emergence in biology and social sciences
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      Lagrangian mean curvature flow
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      Finite geometries: pure mathematics close to applications
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      Quantum symmetry
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      Describing distance: from the plane to spectral triples
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      The Enigma behind the Good–Turing formula
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      C∗-algebras: structure and classification
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      Quantum symmetry
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      Determinacy versus indeterminacy
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      Random matrix theory: Dyson Brownian motion
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      Is it possible to predict the far future before the near future is known accurately?
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      The Interaction of Curvature and Topology
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      The Mathematics of Fluids and Solids
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      Formation Control and Rigidity Theory
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      Nonlinear Acoustics
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      Positive Scalar Curvature and Applications
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      Mixed volumes and mixed integrals
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      Tropical geometry
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      Computing with symmetries
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      Topological recursion
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      Solving quadratic equations in many variables
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      Mathematics plays a key role in scientific computing
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      Spaces of Riemannian metrics
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      Computational Optimal Transport
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      A few shades of interpolation
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      Molecular quantum dynamics
      Marco Radeschi
      Closed geodesics on surfaces and Riemannian manifolds
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      Aperiodic Order and Spectral Properties
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      News on quadratic polynomials
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      Towards a Mathematical Theory of Turbulence in Fluids
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      Profinite groups
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      The adaptive finite element method
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      Footballs and donuts in four dimensions
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      The Willmore Conjecture
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      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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      Chaos and chaotic fluid mixing
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      Friezes and tilings
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      Zero-dimensional symmetry
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      Operator theory and the singular value decomposition
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      The Kadison-Singer problem
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      Howell Tong
      Statistics and dynamical phenomena
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      The ternary Goldbach Problem
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      Matrixfaktorisierungen
      John E. McCarthy
      Dirichlet Series

      Mathematisches Fachgebiet

      Algebra und Zahlentheorie
      Analysis
      Didaktik und Bildung
      Diskrete Mathematik und Grundlagen
      Geometrie und Topologie
      Numerik und Wissenschaftliches Rechnen
      Wahrscheinlichkeitstheorie und Statistik

      Verbindung zu anderen Gebieten

      Chemie und Geowissenschaft
      Informatik
      Ingenieurwissenschaft und Technik
      Finanzwesen
      Geistes- und Sozialwissenschaft
      Biowissenschaft
      Physik
      Überlegungen zur Mathematik

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