Patterns and waves in theory, experiment, and application

Oberwolfach'tan

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.

If you are interested in translating this Snapshot, please contact us at info@imaginary.org

Matematiksel konular

Analiz
Nümerik ve Hesap Analizi

Yazar(lar)

Jason J. Bramburger

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2023-001-EN

PDF indir

snapshot-2023-001.pdf

PDF

snapshots: overview

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Algebras and quantum games
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The periodic tables of algebraic geometry
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Closed geodesics on surfaces
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Route planning for bacteria
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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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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
Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
Baptiste Rognerud
Invitation to quiver representation and Catalan combinatorics
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Searching for structure in complex data: A modern statistical quest
David Kerr
C∗-algebras: structure and classification
Sara Lamboglia, Martin Ulirsch
From the dollar game to the Riemann-Roch Theorem
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Quantum symmetry
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Vertex-to-Self Trajectories on the Platonic Solids
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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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Mixed-dimensional models for real-world applications
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On Logic, Choices and Games
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Nonlinear Acoustics
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Random permutations
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Counting self-avoiding walks on the hexagonal lattice
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Algebra, matrices, and computers
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Positive Scalar Curvature and Applications
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Diophantine equations and why they are hard
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Mixed volumes and mixed integrals
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A short story on optimal transport and its many applications
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Number theory in quantum computing
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Geometry behind one of the Painlevé III differential equations
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The codimension
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The mathematics of aquatic locomotion
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Tropical geometry
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Topological recursion
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Solving quadratic equations in many variables
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Spaces of Riemannian metrics
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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
Felix Günther
Winkeltreue zahlt sich aus
Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
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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
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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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On the containment problem
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Domino tilings of the Aztec Diamond
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Quantum diffusion
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Ideas of Newton-Okounkov bodies
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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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Minimizing energy
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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
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Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
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What does ">" really mean?
Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz
Eğitim ve Eğitim Bilimi
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji
Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

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Matematik Üzerine Düşünceler

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