About me

I am coming to the end of a cotutelle between the Australian National University and l'Université de Paris-Nord XIII jointly supervised by Denis-Charles Cisinski and Amnon Neeman. Previously, I did an M2 (the second year of a masters) at l'Université de Paris-Sud XI, writing a thesis under the supervision of Bruno Kahn, and before that I completed my undergraduate at the University of Western Australia, where I had the good fortune to also participate in some research in finite group theory (cf Publications).

My thesis is in motives, an area of algebraic geometry that aims to find a unifying framework for the many various cohomology theories that exist in various branches of algebraic geometry. More specifically, I am working on replacing the resolution of singularities arguments in Voevodsky's paper “Triangulated categories of motives over a field” with Gabber's theorem on alterations.

Publications

2009. Michael Giudici, Shane Kelly, Characterizing a family of elusive groups. Journal of Group Theory, 12(1).

2007. Shane Kelly, Constructions of intriguing sets of polar spaces from field reduction and derivation. Designs, Codes and Cryptography, 43(1).

2007. John Bamberg, Shane Kelly, Maska Law, Tim Penttila, Tight Sets and m-Ovoids of Polar Spaces. J. Combin. Theory Ser. A, 114(7).

Theses

2008. Fourier-Mukai Transforms in Algebraic Geometry Supervised by Luca Barbieri-Viale.

2007. Homology of Schemes Supervised by Bruno Kahn.

Documents

Selected solutions to various exercises.

An index can be found here.

Here are links to some solutions to various exercises that I did in my first year. For the most-part these are first attempts, or near first attempts, as the goal was usually to keep a record of what I've done rather than to create a neat, ordered, coherent presentation. I put them here on the off-chance that they are useful to somebody.

Hatchers's Algebraic Topology. Section 4.1 Section 4.2 Section 4.3
Liu's Algebraic Geometry and Arithmetic Curves. Section 1.1.2
Humphrey's Linear Algebraic Groups. Sections 7 to 20
Hartshorne's Algebraic Geometry. Section II.1 Section II.2 Section II.3 Section II.4 Section II.5 Section II.6 Section II.7 Section II.8 Chapter III

Personal notes for talks I've given.

These are notes that I created for my own sake for various talks that I've given between 2007 and 2009, together with a couple of slides. Even though they were only for me to keep my place I have tried to include references where relevant. There is absolutely NO original material here.

February 2009 Semihomogeneous Sheaves on Abelian Varieties
April 2008 Cohomological Descent
May 2008 A proof of the Grothendieck-Riemann-Roch Theorem
February 2008 Sheaves don't belong to algebraic geometry.
August 2007 Applications of Finite Geometry