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Classification of $C^*$-algebras and $*$-homomorphisms.
KK-Theory, connectivity and unsuspended E-theory, Cuntz semigroups.
Approximation and dimension theory; quasidiagonality. $W^*$-algebras.
Graph $C^*$-algebras and path groupoids. Groupoid modeling of $C^*$-algebras.
Higher category theory. $\infty$-categories and homotopy theory.
Former student in Mathematical Physics. (Outdated!)
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