My research is in operator algebras, particularly the structure and classification of separable nuclear C*-algebras and the construction of examples with novel properties. The Toms–Winter conjecture, formulated with Wilhelm Winter around 2008, predicts the equivalence of three regularity properties for simple separable nuclear C*-algebras: finite nuclear dimension, Z-stability, and strict comparison. The proof of the conjecture was recently completed both by humans and by Open AI, and gives a tripartite characterization of those simple separable amenable C*-algebras which can be classified by Elliott's invariant (K-theory and traces).
My current work focuses on uniform property Γ, matrix geometry, and dimension-growth phenomena in nuclear C*-algebras, and leverages tools from algebraic geometry and differential topology.
My papers can be found on the arXiv or MathSciNet.
This work is currently funded by a Simons Foundation International grant administered by the Simons Foundation [SFI-MPS-TSM-00025606, A.S.T.].