Five ways to spell ADE

Instantanés de recherche mathématique à Oberwolfach

Five ways to spell ADE

The solutions to a surprising number of mathematical questions can be classified by the ADE Coxeter–Dynkin diagrams. This snapshot will show you a selection of these questions and how they correspond to the ADE Coxeter–Dynkin diagrams.

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Sujet mathématique

Algèbre et théorie des nombres
Géométrie et Topologie

Liens avec d'autres domaines

Pensées mathématiques

Auteur(s)

Dani Kaufman

Licence

DOI

10.14760/SNAP-2025-003-EN

Télécharger PDF

snapshot-2025-003.pdf

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snapshots: overview

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The five Platonic solids and their connection to root systems
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Five ways to spell ADE
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Convex polytopes and linear programs
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Truncated fusion rules for supergroups
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Waves and incidences
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Geproci sets: a new perspective in algebraic geometry
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The geometry of fair division
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4 = 2 × 2, or the power of even integers in Fourier analysis
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Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains
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Algebras and quantum games
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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
Fabian Mussnig
Characterizations of intrinsic volumes on convex bodies and convex functions
Jennifer S. Balakrishnan
A tale of three curves
Michael Baake, Uwe Grimm, Robert V. Moody
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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Solving inverse problems with Bayes’ theorem
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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
Jason D. Lotay
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
Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
Anna Haensch
Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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Invitation to quiver representation and Catalan combinatorics
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Searching for structure in complex data: A modern statistical quest
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C∗-algebras: structure and classification
Sara Lamboglia, Martin Ulirsch
From the dollar game to the Riemann-Roch Theorem
Steven Rayan, Laura P. Schaposnik
Higgs bundles without geometry
Behrend Heeren, Martin Rumpf
Shape space - a paradigm for character animation in computer graphics
Joshua Zahl
Rotating needles, vibrating strings, and Fourier summation
Moritz Weber
Quantum symmetry
Christian Berg
Determinacy versus indeterminacy
Jayadev S. Athreya, David Aulicino
Vertex-to-Self Trajectories on the Platonic Solids
Gianluca Finocchio
Random matrix theory: Dyson Brownian motion
Holger Kammeyer, Roman Sauer
From Betti numbers to l2-Betti numbers
Martin J. Gander
Is it possible to predict the far future before the near future is known accurately?
Jan-Bernhard Kordaß
The Interaction of Curvature and Topology
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The Mathematics of Fluids and Solids
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A surprising connection between quantum mechanics and shallow water waves
Daniel Zelazo, Shiyu Zhao
Formation Control and Rigidity Theory
Ana Khukhro
Expander graphs and where to find them
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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
Pietro Milici
Touching the transcendentals: tractional motion from the birth of calculus to future perspectives
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Configuration spaces and braid groups
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Limits of graph sequences
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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
Jonathan Rosenberg, David Wraith
Positive Scalar Curvature and Applications
Hector Pasten
Diophantine equations and why they are hard
Martin Buhmann, Janin Jäger
On radial basis functions
Ralf Schiffler
Snake graphs, perfect matchings and continued fractions
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Estimating the volume of a convex body
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Mixed volumes and mixed integrals
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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 Complexity, Robotics and Social Choice
Thomas Sauer
Prony’s method: an old trick for new problems
Colva M. Roney-Dougal
Computing with symmetries
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Topological recursion
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The Algebraic Statistics of an Oberwolfach Workshop
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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
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Computational Optimal Transport
Justyna Szpond
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
Lukas Pottmeyer
News on quadratic polynomials
Felix Günther
Winkeltreue zahlt sich aus
Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
Laurent Bartholdi
Profinite groups
Dietmar Gallistl
The adaptive finite element method
Steven Klee
Footballs and donuts in four dimensions
Nikolai Nowaczyk
The Willmore Conjecture
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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Anthony T Patera, Karsten Urban
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Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
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Quantum diffusion
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Jürg Kramer, Anna-Maria Pippich
Special values of zeta functions and areas of triangles
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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
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
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Arrangements of lines
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Harald Helfgott
The ternary Goldbach Problem
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Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Sujet mathématique

Algèbre et théorie des nombres
Analyse
Pédagogie et éducation
Mathématiques discrètes et fondements des mathématiques
Géométrie et Topologie
Calcul numérique et calcul scientifique
Théorie des probabilités et statistique

Liens avec d'autres domaines

Chimie et sciences de la terre
Informatique
Ingénierie et technologie
Finances
Humanités et sciences sociales
Sciences de la vie
Physique
Pensées mathématiques

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