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1.
Low-dimensional topology: the study of knots,
three-manifolds, four-manifolds, knot cobordism
etc.
2.
Topological invariants associated to quantum field
theory (i.e. "Quantum invariants"), such as quantum group
invariants, finite-type invariants, the Kontsevich
integral and categorical invariants.
3.
Lie algebras, Lie groups and representation theory.
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