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Quantum symmetry

Snapshots of modern mathematics from Oberwolfach

Quantum symmetry

In mathematics, symmetry is usually captured using the formalism of groups. However, the developments of the past few decades revealed the need to go beyond groups: to “quantum groups”. We explain the passage from spaces to quantum spaces, from groups to quantum groups, and from symmetry to quantum symmetry, following an analytical appr

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Mathematical subjects

Algebra and Number Theory
Analysis

Connections to other fields

Physics

Author(s)

Moritz Weber

License

DOI (Digital Object Identifier)

10.14760/SNAP-2020-005-EN

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snapshots-2020-005.pdf

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snapshots: overview

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      The geometry of fair division
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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
      Jason J. Bramburger
      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
      Jennifer S. Balakrishnan
      A tale of three curves
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      What is Pattern?
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      Biological Shape Analysis with Geometric Statistics and Learning
      Ilya Dumanski, Valentina Kiritchenko
      Representations and degenerations
      Jonas Latz, Björn Sprungk
      Solving inverse problems with Bayes’ theorem
      Herbert Gangl
      Jewellery from tessellations of hyperbolic space
      Chr istina Frederick, Yunan Yang
      Seeing through rock with help from optimal transport
      David A. Craven
      Searching for the Monster in the Trees
      Hugh Thomas
      The Robinson–Schensted algorithm
      Franca Hoffmann, Sara Merino-Aceituno
      Emergence in biology and social sciences
      Jason D. Lotay
      Lagrangian mean curvature flow
      Leo Storme
      Finite geometries: pure mathematics close to applications
      Francesca Arici, Bram Mesland
      Describing distance: from the plane to spectral triples
      Martijn Caspers
      Quantum symmetry
      Fadoua Balabdaoui, Yulia Kulagina
      The Enigma behind the Good–Turing formula
      Anna Haensch
      Reflections on hyperbolic space
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      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
      David Kerr
      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
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      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
      barbara Kaltenbacher, Igor Kukavica, Irena Lasiecka, Roberto Triggianti, Amjad Fuffaha, Justin Weber
      The Mathematics of Fluids and Solids
      Jake Fillman, Tom van den Boom
      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
      Simon Arridge, Maarten de Hoop, Peter Maass, Ozan Öktem, Carola Schönlie, Michael Unser
      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
      Loïc Petitgirard
      Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
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      Configuration spaces and braid groups
      Tereza Klimošová
      Limits of graph sequences
      Paulo Oliva
      On Logic, Choices and Games
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      Nonlinear Acoustics
      Volker Betz
      Random permutations
      Hugo Duminil-Copin
      Counting self-avoiding walks on the hexagonal lattice
      A. S. Detinko, D. L. Flannery, A. Hulpke
      Algebra, matrices, and computers
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      Positive Scalar Curvature and Applications
      Hector Pasten
      Diophantine equations and why they are hard
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      On radial basis functions
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      Snake graphs, perfect matchings and continued fractions
      Nicolai Baldin
      Estimating the volume of a convex body
      Liran Rotem
      Mixed volumes and mixed integrals
      Filippo Santambrogio
      A short story on optimal transport and its many applications
      Sebastian Schönnenbeck
      Number theory in quantum computing
      Matthias Morzfeld, Sebastian Reich
      Data assimilation: mathematics for merging models and data
      Claus Hertling
      Geometry behind one of the Painlevé III differential equations
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      The codimension
      Marius Tucsnak
      The mathematics of aquatic locomotion
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      Tropical geometry
      Alex Barnett
      Fast Solvers for Highly Oscillatory Problems
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      Topological Complexity, Robotics and Social Choice
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      Prony’s method: an old trick for new problems
      Colva M. Roney-Dougal
      Computing with symmetries
      Piotr Sułkowski
      Topological recursion
      Anna Seigal
      The Algebraic Statistics of an Oberwolfach Workshop
      Jean-Pierre Tignol
      Solving quadratic equations in many variables
      Chi-Wang Shu
      Mathematics plays a key role in scientific computing
      Mauricio Bustamante, Jan-Bernhard Kordaß
      Spaces of Riemannian metrics
      Shaula Fiorelli Vilmart, Gilles Vilmart
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      Justin Solomon
      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
      Lior Bary-Soroker
      Prime Tuples in Function Fields
      Rafael Guglielmetti, Matthieu Jacquemet
      Polyhedra and commensurability
      Manfred Deistler, Andreas Graef
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      Eugenio Giannelli, Jay Taylor
      Symmetry and characters of finite groups
      Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
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      Tomasz Szemberg
      On the containment problem
      Éric Fusy
      Random sampling of domino and lozenge tilings
      Magnus Egerstedt
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      Juanjo Rué
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      Sebastian Funk
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      Quantum diffusion
      Amanda Swan, Albert Murtha
      Modelling the spread of brain tumours
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      Visual Analysis of Spanish Male Mortality
      Christopher Sangwin
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      Jürg Kramer, Anna-Maria Pippich
      Special values of zeta functions and areas of triangles
      Victoria Powers
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      Ideas of Newton-Okounkov bodies
      Ben Schweizer
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      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
      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
      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

      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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