Positive Scalar Curvature and Applications

Snapshots of modern mathematics from Oberwolfach

Positive Scalar Curvature and Applications

We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature. We discuss why this is interesting and how it relates to general relativity.

Also available in Spanish.

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Mathematical subjects

Geometry and Topology

Connections to other fields

Physics

Author(s)

Jonathan Rosenberg, David Wraith

License

DOI (Digital Object Identifier)

10.14760/SNAP-2019-004-EN

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snapshots-2019-004.pdf

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snapshots: overview

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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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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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Computational Optimal Transport
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A few shades of interpolation
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Molecular quantum dynamics
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Closed geodesics on surfaces and Riemannian manifolds
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Aperiodic Order and Spectral Properties
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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
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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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Quantum diffusion
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Zero-dimensional symmetry
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Billiards and flat surfaces
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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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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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