Patterns and waves in theory, experiment, and application

Instantáneas de la actualidad matemática desde 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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Área matemática

Análisis
Cálculo numérico y científico

Autor(es)

Jason J. Bramburger

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2023-001-EN

Descargar PDF

snapshot-2023-001.pdf

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snapshots: overview

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Algebras and quantum games
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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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Representations and degenerations
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Jewellery from tessellations of hyperbolic space
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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The Mathematics of Fluids and Solids
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Formation Control and Rigidity Theory
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Random permutations
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Algebra, matrices, and computers
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Positive Scalar Curvature and Applications
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Topological recursion
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Computational Optimal Transport
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A few shades of interpolation
George Hagedorn, Caroline Lasser
Molecular quantum dynamics
Marco Radeschi
Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
Mathematische Modellierung von Krebswachstum
Michael Baake, David Damanik, Uwe Grimm
Aperiodic Order and Spectral Properties
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News on quadratic polynomials
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Winkeltreue zahlt sich aus
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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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Quantum diffusion
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Friezes and tilings
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Zero-dimensional symmetry
Christine Breiner
Minimizing energy
Diana Davis
Billiards and flat surfaces
Peter Benner, Hermann Mena, René Schneider
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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
Brian Harbourne, Thomas Szemberg
Arrangements of lines
Bruce Reznick
What does ">" really mean?
Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Área matemática

Álgebra y Teoría de números
Análisis
Didáctica y Educación
Matemática discreta y Fundamentos
Geometría y Topología
Cálculo numérico y científico
Teoría de la probabilidad y Estadística

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Química y Ciencias de la Tierra
Informática
Ingeniería y Tecnología
Finanzas
Humanidades y Ciencias sociales
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