Topological Complexity, Robotics and Social Choice

Schnappschüsse moderner Mathematik aus 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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Mathematisches Fachgebiet

Geometrie und Topologie

Verbindung zu anderen Gebieten

Ingenieurwissenschaft und Technik

Geistes- und Sozialwissenschaft

Autor(en)

Greg Lupton, John Oprea, José Gabriel Carrasquel Vera

Lizenz

CC BY-SA-4.0

DOI (Digital Object Identifier)

10.14760/SNAP-2018-005-EN

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Quantum symmetry

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Random permutations

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Positive Scalar Curvature and Applications

Diophantine equations and why they are hard

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On radial basis functions

Snake graphs, perfect matchings and continued fractions

Estimating the volume of a convex body

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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Data assimilation: mathematics for merging models and data

Geometry behind one of the Painlevé III differential equations

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The codimension

The mathematics of aquatic locomotion

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Tropical geometry

Fast Solvers for Highly Oscillatory Problems

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Topological Complexity, Robotics and Social Choice

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Computing with symmetries

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Topological recursion

The Algebraic Statistics of an Oberwolfach Workshop

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Solving quadratic equations in many variables

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

Computational Optimal Transport

A few shades of interpolation

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Molecular quantum dynamics

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

Winkeltreue zahlt sich aus

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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

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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High performance computing on smartphones

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Symmetry and characters of finite groups

Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes

Das Problem der Kugelpackung

Tomasz Szemberg

On the containment problem

Random sampling of domino and lozenge tilings

Magnus Egerstedt

Swarming robots

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Domino tilings of the Aztec Diamond

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Quantum diffusion

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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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Chaos and chaotic fluid mixing

Friezes and tilings

Zero-dimensional symmetry

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Minimizing energy

Billiards and flat surfaces

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The Kadison-Singer problem

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Swallowtail on the shore

Statistics and dynamical phenomena

Brian Harbourne, Thomas Szemberg

Arrangements of lines

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The ternary Goldbach Problem

Wolfgang Lerche

Matrixfaktorisierungen

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Dirichlet Series

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