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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

DOI (Digital Object Identifier)

10.14760/SNAP-2018-005-EN

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snapshots-2018-005.pdf

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snapshots: overview

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      Convex polytopes and linear programs
      Thorsten Heidersdorf
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      Waves and incidences
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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
      Vern I. Paulsen
      Algebras and quantum games
      Ingmar Saberi
      Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
      Pieter Belmans
      The periodic tables of algebraic geometry
      Jason J. Bramburger
      Patterns and waves in theory, experiment, and application
      Benjamin Dozier
      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?
      Saiteja Utpala, Nina Miolane
      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
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      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
      Martijn Caspers
      Quantum symmetry
      Francesca Arici, Bram Mesland
      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
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      Ultrafilter methods in combinatorics
      Gandalf Lechner
      Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
      Baptiste Rognerud
      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
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      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
      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)
      Rita Jiménez Rolland, Miguel A. Xicoténcatl
      Configuration spaces and braid groups
      Tereza Klimošová
      Limits of graph sequences
      Paulo Oliva
      On Logic, Choices and Games
      Barbara Kaltenbacher, Rainer Brunnhuber
      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
      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
      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
      Antonio Lerario
      The codimension
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      The mathematics of aquatic locomotion
      Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro
      Tropical geometry
      Alex Barnett
      Fast Solvers for Highly Oscillatory Problems
      Greg Lupton, John Oprea, José Gabriel Carrasquel Vera
      Topological Complexity, Robotics and Social Choice
      Thomas Sauer
      Prony’s method: an old trick for new problems
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      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
      Computing the long term evolution of the solar system with geometric numerical integrators
      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
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      Aperiodic Order and Spectral Properties
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      News on quadratic polynomials
      Felix Günther
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      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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      High performance computing on smartphones
      Eugenio Giannelli, Jay Taylor
      Symmetry and characters of finite groups
      Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
      Das Problem der Kugelpackung
      Tomasz Szemberg
      On the containment problem
      Éric Fusy
      Random sampling of domino and lozenge tilings
      Magnus Egerstedt
      Swarming robots
      Ulrich Krähmer
      From computer algorithms to quantum field theory: an introduction to operads
      Juanjo Rué
      Domino tilings of the Aztec Diamond
      Sebastian Funk
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      Quantum diffusion
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      Modelling the spread of brain tumours
      J. Marron
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      Jürg Kramer, Anna-Maria Pippich
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      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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      Operator theory and the singular value decomposition
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      The Kadison-Singer problem
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      Howell Tong
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      John E. McCarthy
      Dirichlet Series

      Mathematisches Fachgebiet

      Algebra und Zahlentheorie
      Analysis
      Didaktik und Bildung
      Diskrete Mathematik und Grundlagen
      Geometrie und Topologie
      Numerik und Wissenschaftliches Rechnen
      Wahrscheinlichkeitstheorie und Statistik

      Verbindung zu anderen Gebieten

      Chemie und Geowissenschaft
      Informatik
      Ingenieurwissenschaft und Technik
      Finanzwesen
      Geistes- und Sozialwissenschaft
      Biowissenschaft
      Physik
      Überlegungen zur Mathematik

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