Quantum Groups and Noncommutative Geometry

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Research topics

  • Dirac operators on quantum homogeneous spaces, construction of spectral triples, and applications to models in mathematical physics.
  • Noncommutative generalization of Borsuk-Ulam and Brouwer fixed-point theorems, and non-contractibility of compact quantum groups.
  • Index theory, invariants of elliptic operators, applications of noncommutative geometry and KK-theory (bounded and unbounded) to the study of the geometry and topology of manifolds.
  • ADHM construction of noncommutative instatons in SUq(2) gauge theories. Non commutative moduli spaces.
  • Representations of SUq(2) at roots of unity and extensions of the spin covering with applications to exotic statistics.


Research Group

Visiting Professors


Main External Collaborators


Weekly seminar of the group of Noncommutative Geometry, SISSA and Università di Trieste. Noncommutative geometry, a blog on noncommutative Geometry., noncommutative Geometry and particle Physics blog.


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