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. All but the implication from strict comparison to Z-stability are now known in full generality. Drop me a line if you figure it out.
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.