Topological Complexity, Robotics and Social Choice

Instantáneas de la actualidad matemática desde Oberwolfach

Topological Complexity, Robotics and Social Choice

Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the wider area of Applied Algebraic Topology. Surprisingly, the same mathematics gives insight into the question of creating social choice functions, which may be viewed as algorithms for making decisions by artificial intelligences.

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Área matemática

Geometría y Topología

Relaciones con otros campos

Ingeniería y Tecnología
Humanidades y Ciencias sociales

Autor(es)

Greg Lupton, John Oprea, José Gabriel Carrasquel Vera

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2018-005-EN

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snapshots-2018-005.pdf

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snapshots: overview

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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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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?
Saiteja Utpala, Nina Miolane
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Representations and degenerations
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Jewellery from tessellations of hyperbolic space
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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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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
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Reflections on hyperbolic space
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Quantum symmetry
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Nonlinear Acoustics
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Random permutations
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Algebra, matrices, and computers
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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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Fast Solvers for Highly Oscillatory Problems
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Topological Complexity, Robotics and Social Choice
Thomas Sauer
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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
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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
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Polyhedra and commensurability
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Ben Schweizer
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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
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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
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Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

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