The Interaction of Curvature and Topology

Snapshots of modern mathematics from Oberwolfach

The Interaction of Curvature and Topology

In this snapshot we will outline the mathematical notion of curvature by means of comparison geometry. We will then try to address questions as the ways in which curvature might influence the topology of a space, and vice versa.

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Mathematical subjects

Geometry and Topology

Author(s)

Jan-Bernhard Kordaß

License

DOI (Digital Object Identifier)

10.14760/SNAP-2019-020-EN

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snapshots-2019-020.pdf

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snapshots: overview

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The geometry of fair division
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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
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Patterns and waves in theory, experiment, and application
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Closed geodesics on surfaces
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Route planning for bacteria
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Characterizations of intrinsic volumes on convex bodies and convex functions
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A tale of three curves
Michael Baake, Uwe Grimm, Robert V. Moody
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
Chr istina Frederick, Yunan Yang
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
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
Isaac Goldbring
Ultrafilter methods in combinatorics
Gandalf Lechner
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
Baptiste Rognerud
Invitation to quiver representation and Catalan combinatorics
Po-Ling Loh
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
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Quantum symmetry
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Determinacy versus indeterminacy
Jayadev S. Athreya, David Aulicino
Vertex-to-Self Trajectories on the Platonic Solids
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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?
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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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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
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Touching the transcendentals: tractional motion from the birth of calculus to future perspectives
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Configuration spaces and braid groups
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Limits of graph sequences
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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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Algebra, matrices, and computers
Jonathan Rosenberg, David Wraith
Positive Scalar Curvature and Applications
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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
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Estimating the volume of a convex body
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Mixed volumes and mixed integrals
Filippo Santambrogio
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
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Geometry behind one of the Painlevé III differential equations
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The codimension
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The mathematics of aquatic locomotion
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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
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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
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
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
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Prime Tuples in Function Fields
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Polyhedra and commensurability
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Robert Altmann, Jan Heiland
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Anthony T Patera, Karsten Urban
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
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Ulrich Krähmer
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Domino tilings of the Aztec Diamond
Sebastian Funk
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Quantum diffusion
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Ideas of Newton-Okounkov bodies
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Darcy’s law and groundwater flow modelling
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Modelling communication and movement: from cells to animals and humans
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Chaos and chaotic fluid mixing
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Friezes and tilings
George Willis
Zero-dimensional symmetry
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Minimizing energy
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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
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Swallowtail on the shore
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Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
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The ternary Goldbach Problem
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Matrixfaktorisierungen
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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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