Alastair Craw

Alastair Craw is a Professor in the Department of Mathematical Sciences at the University of Bath. His work bridges algebraic geometry and representation theory, focusing on moduli spaces of quiver representations, derived categories, and noncommutative algebraic geometry.

• Research themes include geometric interpretations of the McKay correspondence and connections to Bridgeland stability manifolds.
• Current projects involve extending categorical equivalences to broader geometric frameworks.

His research often applies explicit methods to problems in toric geometry, crepant resolutions, and quiver varieties. Projects funded by the Leverhulme Trust and the Engineering and Physical Sciences Research Council underscore his leadership in pure mathematics.

Recent work explores GIT quotients, Cox rings, and birational geometry of quiver varieties, with a focus on unifying abstract and geometric approaches. This aligns with his broader goal of translating algebraic structures into geometric insights.

Grants and supervision activities highlight his active role in advancing research. As a Principal Investigator, he has led two major projects, and his group’s outputs address foundational questions in algebraic geometry.