Alastair Craw

Biography

Alastair Craw is a professor belongs to the department of Mathematical Sciences from the university of Bath.

Research Interest

My research interests lie in pure mathematics, and specifically in algebraic geometry and representation theory. Much of my research applies explicit methods to improve our understanding of moduli spaces of quiver representations and their derived categories. One motivating question is to ask for nice moduli descriptions of well known varieties. This is now understood for projective toric varieties and, more generally, for Mori Dream Spaces. This leads naturally to the study of multigraded linear series (also known as framed quiver varieties or quiver flag varieties) as ambient spaces in noncommutative algebraic geometry.Another theme of my research is to understand which algebraic varieties carry tilting bundles, thereby providing an explicit understanding of their derived category of coherent sheaves. The first known examples were provided by Beilinson and Kapranov, while many of the more recent examples have been influenced by the McKay correspondence in one form or another. Examples include framed quiver varieties, G-Hilbert schemes, moduli spaces arising in the study of consistent dimer model algebras, and smooth toric Fano varieties in low dimensions. These constructions lead to interesting questions about mutation, wall crossing phenomena and Bridgeland stability manifolds.