Uploaded February 2026 | Updated September 2026, 2 weeks ago
Speaker: Réamonn Ó Buachalla (Charles University, Prague)
Abstract: This talk opens with a brief introduction to noncommutative geometry, emphasizing C*-algebraic Gelfand duality as a framework for viewing noncommutative algebras as function algebras on quantum spaces. We recall the standard q-sphere, or Podleś sphere, as a central example of a quantum homogeneous space. We explain how the Podleś sphere admits a direct q-deformation of the classical complex geometry of the two-sphere, and how this connects quantum groups and Alain Connes’s theory of spectral triples. Time permitting we discuss how this work extends to the setting of the cominiscule quantum flag manifolds.
Speaker: Réamonn Ó Buachalla (Charles University, Prague)
Abstract: This talk opens with a brief introduction to noncommutative geometry, emphasizing C*-algebraic Gelfand duality as a framework for viewing noncommutative algebras as function algebras on quantum spaces. We recall the standard q-sphere, or Podleś sphere, as a central example of a quantum homogeneous space. We explain how the Podleś sphere admits a direct q-deformation of the classical complex geometry of the two-sphere, and how this connects quantum groups and Alain Connes’s theory of spectral triples. Time permitting we discuss how this work extends to the setting of the cominiscule quantum flag manifolds.
