Footballs and donuts in four dimensions

Snapshots of modern mathematics from Oberwolfach

Footballs and donuts in four dimensions

In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions. 

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Mathematical subjects

Discrete Mathematics and Foundations
Geometry and Topology

Connections to other fields

Computer Science
Engineering and Technology

Author(s)

Steven Klee

License

DOI (Digital Object Identifier)

10.14760/SNAP-2016-012-EN

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snapshot-2016-012-klee.pdf

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snapshots: overview

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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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The Robinson–Schensted algorithm
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Finite geometries: pure mathematics close to applications
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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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Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
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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
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From the dollar game to the Riemann-Roch Theorem
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Higgs bundles without geometry
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Shape space - a paradigm for character animation in computer graphics
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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
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The Interaction of Curvature and Topology
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The mathematics of aquatic locomotion
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Topological recursion
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Computational Optimal Transport
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Molecular quantum dynamics
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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
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The Willmore Conjecture
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Prime Tuples in Function Fields
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Quantum diffusion
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Zero-dimensional symmetry
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The Kadison-Singer problem
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The ternary Goldbach Problem
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Matrixfaktorisierungen
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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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