(Operator Algebras) Elliott's program to classify simple separable nuclear C*-algebras via K-theory and traces is essentially complete module the necessary regularity assumptions of Z-stability and the Universal coefficient theorem. My aim is to move beyond the classifiable case and tackle the obstructions which appear when studying normal operators acting on separable Hilbert spaces in the framework of a unital C*-algebra of stable rank one. Whether it require more delicate invariants such as the Cuntz semigroup, or specialized tools in algebraic topology, I study the fine structures which help distinguish any two well-behaved algebras.
In preparation:
New structure for Villadsen algebras of the first type, 2026
Rordam's question about the embeddings of the Jiang-Su algebra, 2026
An existence theorem for *-homomorphisms out of the circle algebra, 2026