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Algebra, matrices, and computers

Instantáneas de la actualidad matemática desde Oberwolfach

Algebra, matrices, and computers

What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that rely on the theory of matrix groups and new methods for handling matrix groups in a computer.

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Área matemática

Álgebra y Teoría de números

Relaciones con otros campos

Informática

Autor(es)

A. S. Detinko, D. L. Flannery, A. Hulpke

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2019-005-EN

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snapshots-2019-005.pdf

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snapshots: overview

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      Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains
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      The periodic tables of algebraic geometry
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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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      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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      Describing distance: from the plane to spectral triples
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      Quantum symmetry
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      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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      Rotating needles, vibrating strings, and Fourier summation
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      Quantum symmetry
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      Determinacy versus indeterminacy
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      Vertex-to-Self Trajectories on the Platonic Solids
      Gianluca Finocchio
      Random matrix theory: Dyson Brownian motion
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      From Betti numbers to l2-Betti numbers
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      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
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      Formation Control and Rigidity Theory
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      Expander graphs and where to find them
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      Mixed-dimensional models for real-world applications
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      Configuration spaces and braid groups
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      Limits of graph sequences
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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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      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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      The codimension
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      Tropical geometry
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      Topological Complexity, Robotics and Social Choice
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      Computing with symmetries
      Piotr Sułkowski
      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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      Computing the long term evolution of the solar system with geometric numerical integrators
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      Computational Optimal Transport
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      Molecular quantum dynamics
      Marco Radeschi
      Closed geodesics on surfaces and Riemannian manifolds
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      Mathematische Modellierung von Krebswachstum
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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
      Steven Klee
      Footballs and donuts in four dimensions
      Nikolai Nowaczyk
      The Willmore Conjecture
      Lior Bary-Soroker
      Prime Tuples in Function Fields
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      Polyhedra and commensurability
      Manfred Deistler, Andreas Graef
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      Symmetry and characters of finite groups
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      On the containment problem
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      Random sampling of domino and lozenge tilings
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      Swarming robots
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      From computer algorithms to quantum field theory: an introduction to operads
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      Domino tilings of the Aztec Diamond
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      The mystery of sleeping sickness – why does it keep waking up?
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      Quantum diffusion
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      Modelling the spread of brain tumours
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      Visual Analysis of Spanish Male Mortality
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      Special values of zeta functions and areas of triangles
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      Tom Solomon
      Chaos and chaotic fluid mixing
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      Zero-dimensional symmetry
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      Minimizing energy
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      Operator theory and the singular value decomposition
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      Matrixfaktorisierungen
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      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

      Relaciones con otros campos

      Química y Ciencias de la Tierra
      Informática
      Ingeniería y Tecnología
      Finanzas
      Humanidades y Ciencias sociales
      Ciencias de la vida
      Física
      Reflexiones sobre la matemática

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