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Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften

Schnappschüsse moderner Mathematik aus Oberwolfach

Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften

Wir werden einige grundlegende Ideen der Eichtheorie und der dazugehörigen Differentialtopologie erkunden. Damit kann sich die Leserin ein Bild des Modulraums flacher Zusammenhänge machen und ihn mit den physikalisch motivierten Ideen dahinter in Beziehung bringen. Den Begriffen von Symmetrien und Feldern gehen wir gründlich nach. Außerdem werfen wir einen flüchtigen Blick auf unendliche Symmetrie in zwei Dimensionen und auf vor kurzem entdeckte Verallgemeinerungen.

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Mathematisches Fachgebiet

Geometrie und Topologie

Verbindung zu anderen Gebieten

Physik

Autor(en)

Ingmar Saberi

Lizenz

DOI (Digital Object Identifier)

10.14760/SNAP-2023-003-EN

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snapshot-2023-003.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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      Jason J. Bramburger
      Patterns and waves in theory, experiment, and application
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      Closed geodesics on surfaces
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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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      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
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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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      Invitation to quiver representation and Catalan combinatorics
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      C∗-algebras: structure and classification
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      Quantum symmetry
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      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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      Formation Control and Rigidity Theory
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      Nonlinear Acoustics
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      Random permutations
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      Positive Scalar Curvature and Applications
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      Diophantine equations and why they are hard
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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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      Data assimilation: mathematics for merging models and data
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      Tropical geometry
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      Computing with symmetries
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      Topological recursion
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      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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      Computational Optimal Transport
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      Molecular quantum dynamics
      Marco Radeschi
      Closed geodesics on surfaces and Riemannian manifolds
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      Profinite groups
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      The adaptive finite element method
      Steven Klee
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      The Willmore Conjecture
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      Manfred Deistler, Andreas Graef
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      Christine Breiner
      Minimizing energy
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      The Kadison-Singer problem
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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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