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Positive Scalar Curvature and Applications

Schnappschüsse moderner Mathematik aus 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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Mathematisches Fachgebiet

Geometrie und Topologie

Verbindung zu anderen Gebieten

Physik

Autor(en)

Jonathan Rosenberg, David Wraith

Lizenz

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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      Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
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      The periodic tables of algebraic geometry
      Jason J. Bramburger
      Patterns and waves in theory, experiment, and application
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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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      A tale of three curves
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      What is Pattern?
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      Representations and degenerations
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      Jewellery from tessellations of hyperbolic space
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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
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      Lagrangian mean curvature flow
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      Finite geometries: pure mathematics close to applications
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      Describing distance: from the plane to spectral triples
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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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      Invitation to quiver representation and Catalan combinatorics
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      Rotating needles, vibrating strings, and Fourier summation
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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
      Gianluca Finocchio
      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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      Nonlinear Acoustics
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      Random permutations
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      Algebra, matrices, and computers
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      Positive Scalar Curvature and Applications
      Hector Pasten
      Diophantine equations and why they are hard
      Martin Buhmann, Janin Jäger
      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
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      Number theory in quantum computing
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      Geometry behind one of the Painlevé III differential equations
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      The codimension
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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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      Prony’s method: an old trick for new problems
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      Computing with symmetries
      Piotr Sułkowski
      Topological recursion
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      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
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      Spaces of Riemannian metrics
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      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
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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
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      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
      The mystery of sleeping sickness – why does it keep waking up?
      Antti Knowles
      Quantum diffusion
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      Modelling the spread of brain tumours
      J. Marron
      Visual Analysis of Spanish Male Mortality
      Christopher Sangwin
      Curriculum development in university mathematics: where mathematicians and education collide
      Jürg Kramer, Anna-Maria Pippich
      Special values of zeta functions and areas of triangles
      Victoria Powers
      How to choose a winner : the mathematics of social choice
      Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
      Ideas of Newton-Okounkov bodies
      Ben Schweizer
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      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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      Gregory Knese
      Operator theory and the singular value decomposition
      Alain Valette
      The Kadison-Singer problem
      Ragnar-Olaf Buchweitz, Eleonore Faber
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      Howell Tong
      Statistics and dynamical phenomena
      Brian Harbourne, Thomas Szemberg
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      Bruce Reznick
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      Harald Helfgott
      The ternary Goldbach Problem
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      Matrixfaktorisierungen
      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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