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Research

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    • Prof. Dr. Catherine Meusburger
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Research

Reseach Summary

My research interests are at the interface of algebra and mathematical physics. More specifically, I am interested in mathematical structures arising in three-dimensional gravity, Chern-Simons theory and quantum geometry. These interest of these research subjects is that they tie together a variety of topics from algebra, geometry and topology:

Algebra

  • Poisson-Lie groups
  • Hopf algebras and quantum groups
  • representation theory of Lie groups and quantum groups
  • (braided) monoidal categories and higher categories
  • braid groups and mapping class groups
  • Fuchsian groups

Geometry

  • Moduli spaces of flat connections
  • Poisson and symplectic geometry
  • Teichmüller theory
  • differential geometry in three dimensions
  • hyperbolic geometry in two and three dimensions

Topology

  • link and knot invariants
  • quantum invariants of manifolds contructed from representation theory
  • topological quantum field theories
Friedrich-Alexander-Universität
Erlangen-Nürnberg

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91054 Erlangen
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