DPhil

• (2012) A copy of my submitted DPhil thesis on Free curves on varieties (November 2012). Note a number of mistakes have been corrected in the published version.

• (2012) A very short paper on an example of an MRC quotient in characteristic p with large fundamental group.

• (2010) Transfer dissertation: One section with bits and pieces on arithmetic fundamental groups and the section conjecture and another section on the geometry of del Pezzo surfaces and the Brauer-Manin obstruction to the existence of rational points.

Notes

• (2011) Gabber's Theorem on Brauer Groups of Schemes Notes that I started writing up a proof of the isomorphism Br(X) = Br'(X) when X is an affine or quasi-projective scheme following Hoobler's and de Jong's papers. The latter case is still incomplete.

• (2009) The Brauer-Manin obstruction: Notes that I wrote for a talk in the Junior Geometry and Topology seminar on the Brauer-Manin obstruction.

• (2009) The BSD Conjecture, Regulators and Special Values of L-Functions: Notes I wrote for a talk in the Junior Number Theory seminar on the Birch and Swinnerton-Dyer conjecture. The idea was to get a feeling for higher regulators and the Beilinson/Bloch/Deligne conjectures on special values of L-functions.

Talks

• (2010) Short notes for a talk in the Junior Number Theory seminar about complex multiplication for elliptic curves and class field theory here.

• (2009) Short notes that I wrote for myself for a talk on model categories and homotopy theory for the homotopical algebraic geometry seminar here.

• (2009) Talk on Group/Galois cohomology for the Junior Number Theory seminar. The exercise sheet here and the outline of the talk here.

MSci

• (2008) The Mordell-Weil Group of Abelian Varieties: Theory on Mordell-Weil groups of abelian varieties, descent on Jacobians of higher genus curves and various calculations. A last chapter on the theory of the Brauer-Manin obstruction (which I have rewritten to a slightly better standard in the notes of 11/6/2009 above).

Undergraduate

• (2007) Final third year thesis on "The Class Group of Function Fields of Transcendence Degree One".

• (2006) Second year suprema project on cryptography. Write-up here.

• (2006) I worked on a UROP project (Undergraduate research opportunities) under the supervision of Dr Jeremy Bradley developing IPC (in haskell) which can be found here. Note that this project has now been incorporated in a larger project SRMC, namely its ipclib library found here.

• (2006) Third year computing group project in medical imaging and data mining. Final report here and code not available:-)

• (2005) First year project on "Solving the Boundary Value Problem Using Iterative Solvers for Ax=b" here