Essential p-dimension of congruence covers of mixed Shimura varieties is bounded below by the p-rank of lattices in unipotent radicals of rational boundary components, giving incompressibility for universal abelian-scheme covers.
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The generalised diagonal dimension of a noncommutative Cartan subalgebra in the C*-algebra of finite-propagation operators on a uniformly locally finite metric space equals the asymptotic dimension of the space.
Every stable UCT Kirchberg algebra has a principal étale groupoid model.
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.
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Functoriality and Weyl Groupoids of Ample C*-Diagonal Pairs
Essential p-dimension of congruence covers of mixed Shimura varieties is bounded below by the p-rank of lattices in unipotent radicals of rational boundary components, giving incompressibility for universal abelian-scheme covers.
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Generalised diagonal dimension and applications to large-scale geometry
The generalised diagonal dimension of a noncommutative Cartan subalgebra in the C*-algebra of finite-propagation operators on a uniformly locally finite metric space equals the asymptotic dimension of the space.
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Principal groupoid models for stable UCT Kirchberg algebras
Every stable UCT Kirchberg algebra has a principal étale groupoid model.
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Nuclear C*-algebras: 99 problems
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.