Twisted Multi-Homogeneous Coordinate Rings in Journal of Algebra vol. 223 (2000).
Noncommutative Rational Double Points in Journal of Algebra vol. 232 (2000).
Morita Dualities and Dualizing Complexes [PDF] with Q.S. Wu and J. Zhang. In Israel Journal of Maths vol. 132 (2002).
Del Pezzo Orders with Rajesh Kulkarni in Advances in Math. vol. 173 (2003).
Noncommutative Coordinate Rings and Stacks [PDF] with Colin Ingalls, in Proc. of the LMS vol. 88 (2004).
Splitting Bundles over Hereditary Orders Comm in Algebra vol. 333(7) (2005) p.2193-9.
The minimal model program for orders over surfaces [PDF] with Colin Ingalls. Inventiones Math. vol. 161 (2005)
Numerically Calabi-Yau orders on surfaces with Rajesh Kulkarni, Journal of the LMS vol. 72 (2005).
Noncommutative cyclic covers and maximal orders on surfaces [PDF] in Mike Artin's 70th birthday issue of Advances in Math. vol. 198(2) (2005)
Canonical Singularities of Orders over Surfaces with Colin Ingalls and Paul Hacking, Proc. of the LMS vol. 98 p. 83-115 (Jan, 2009)
McKay correspondence for canonical orders. Trans. AMS vol. 362 (2010), p. 1765-95
Hilbert schemes for quantum planes are projective. Algebras & Repr. Theory vol. 13 (2010), p. 119-26
Moduli of bundles on exotic del Pezzo orders with Rajesh Kulkarni, American Journal of Math. vol. 133, no. 1, (Feb. 2011) p.273-93
Conic bundles and Clifford algebras with Colin Ingalls. Contemp. Math. vol. 562 (2012) p.53-75
Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry Advances in Mathematics vol. vol. 229 (2012) p.2184-209

Here are some preprints.

Noncommutative Mori contractions and P1-bundles with Adam Nyman on arXiv
Rational curves and ruled orders on surfaces with Kenneth Chan.

Seminar talks

A non-commutative Mori contraction [handout] (Banff 2008) Macaulay assumption is missing from definition of non-commutative smooth projective d-fold
Non-commutative projective geometry (University of Melbourne 2009)
Non-commutative Mori contractions (RIMS 2009)
Singularities in the Mori program for orders [handout] (Simons Center for Geometry and Physics 2011)

Lectures on orders (2010) I will be giving a series of lectures on the theory of orders. The main purpose will be to provide details on ramification theory so that one can read papers on recent work on concerning orders on surfaces. The lectures have been typed up by Boris Lerner and should be appropriate for graduate students. They will be updated roughly every week and the final version will be put up on arXiv.

Interested in doing Honours?
If you are interested in doing an honours project in algebra or geometry, feel free to pop in to my office at any time. Some suggestions for thesis topics.

Past Honours/Masters Students
Antony Orton (2003) wrote an excellent thesis on Algebraic Geometry and the Generalisation of Bezout's Theorem.
Kenneth Chan (2004) wrote a thesis on Riemann surfaces and the Jacobian variety On a proof of Torelli's theorem.
Dave Cock (2004) wrote a thesis on The Weyl algebras.
Piotr Horodynski wrote a thesis on Grobner Bases.
Maiyuran Arumugam (2005) wrote a thesis on A theorem of homological algebra: the Hilbert-Burch theorem.
James Maclaurin (2006) wrote a thesis on The resolution of toric singularities.
Boris Lerner (2007) wrote his thesis on The Brauer-Manin obstruction to the Hasse principle.
Koushik Panda (2007) wrote his thesis on Twisted rings of differential operators on the projective line and the Beilinson-Bernstein theorem.
Nathan Menzies (2007) wrote a thesis entitled An introduction to A-infinity algebras.
Steve Ozvatic (2009) wrote a thesis on Factorisation theory in a non-commutative algebra.
Daniel Smyth (2010) wrote a thesis on Finitely generated powerful pro-p groups.
Anthony Christie (2011) wrote a thesis on Classification of simple plane curve singularities and their Auslander-Reiten quiver.

Current Honours/Masters Students
Matthew Brassil

Postgraduate Students

Kenneth Chan (2010) wrote a thesis entitled Resolving singularities of orders on surfaces.
Hugo Bowne-Anderson (2011) wrote a thesis entitled Explicit construction of orders on surfaces.
Boris Lerner wrote a thesis entitled Line bundles and curves on a del Pezzo order

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MATH5735 Modules and Representation Theory (2012)

Here's the course handout

Assignment 1 is due during the thursday lecture of week 5.
Assignment 2 is due during the thursday lecture of week 10.

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Material for courses taught in the past

Click here for old lecture notes, problem sets etc concerning the following courses:

Higher Algebra: Group and Ring Theory

Group theory

Homology and homological algebra

MATH1141: algebra

MATH1241: algebra

Algebraic geometry

Commutative algebra