My main research area is the representation theory of noncommutative algebras and its connections to various other parts of mathematics, such as algebraic geometry, noncommutative geometry, algebraic topology, knot theory and theoretical physics.
More information can be found here.
People interested in the dimer program click here.
Currently I am investigating Calabi-Yau algebras. These algebras appear in the homological study of 3-dimensional gorenstein singularities and also in the study of superstring theory on calabi yau manifolds. I showed that graded 3-dimensional Calabi-Yau algebras derive from superpotentials and together with Michael Wemyss and Travis Schedler we extended the superpotential method to arbitrary dimensions in the case that the algebra is Koszul. In the case of toric singularities I proved that noncommutative toric crepant resolutions in dimension 3 alway come from dimer models and I studied the connection between the different different consistency conditions for dimer models.
I am co-supervisor of Nick Loughlin
MAS2223/MAS3223: Linear Algebra
MAS3217/MAS8217: Coding Theory