Publications:

• Toric Fano threefolds with terminal singularities
  Tohoku Mathematical Journal, 58 (2006), no. 1, 101-121.
• Toric Fano varieties and convex polytopes
  PhD Thesis, 2006, University of Bath. My supervisor was Dr G K Sankaran.
• A note on palindromic δ-vectors for certain rational polytopes, with Matt Fiset
  Electronic Journal of Combinatorics, 15 (2008), N18.
• Bounds on fake weighted projective space
  Kodai Mathematical Journal, 32 (2009), 197-208.
• On the combinatorial classification of toric log del Pezzo surfaces, with Maximilian Kreuzer and Benjamin Nill
  LMS Journal of Computation and Mathematics, 13 (2010), 33-46.
• Canonical toric Fano threefolds
  Canadian Journal of Mathematics, 62 (2010), no. 6, 1293-1309.
• Roots of Ehrhart polynomials of smooth Fano polytopes, with Gábor Hegedüs
  Discrete and Computational Geometry, 46 (2011), no. 3, 488-499.
• The boundary volume of a lattice polytope, with Gábor Hegedüs
  Bulletin of the Australian Mathematical Society, 85 (2012), 84-104.
• Computational birational geometry of minimal rational surfaces, with Gavin Brown and Daniel Ryder.
• Reflexive polytopes of higher index and the number 12, with Benjamin Nill.

Data and databases:

• Web-based searchable databases of the canonical Fano polytopes and the terminal Fano polytopes in three dimensions, and of the low-index LDP-polygons, are available via the Graded Ring Database.
• A printable list of the terminal Fano polytopes in three dimensions is available in pdf format, in ps format, and as plain text. The C source code for generating the list is available here.
• Tables of the low-index LDP-polygons are here. Plain text copies of the raw data are available here.
• C source code for generating a calssification of Fano n-topes with at worst terminal or canonical singularities is available upon request. (It requires knowledge of the minimal n-topes to obtain a complete classification, but can be used to generate partial classifications -- i.e. lots of examples -- quite easily.)
• C source code for finding the possible weights of n-dimensional Gorenstein Fano weighted projective space with at worst terminal, or canonical, singularities is available here.

Organisation of seminars and conferences:

• Magma workshop on Computational Algebraic Geometry, 8-10 September 2010. School of Mathematics, Loughborough University. A practical workshop to discuss possibilities for extending facilities in Algebraic Geometry in existing computational algebra systems such as Magma.
• Graduate workshop on K3 surfaces and multigraded rings, 6-8 April 2009. Mathematics Institute, University of Warwick. With talks from Juergen Hausen (Tuebingen), Daniel Ryder (Bristol), Katrin Wendland (Augsburg), and graduate participants.
• Whilst at UNB I helped organise several geometry seminars. I was also the UNB organiser for the summer 2007 ASCI seminar series.
• GAeL XIV, 6-11 March 2006. Stephan Banach Centre, Bedlewo, Poland. With principal talks from Frederic Campana (Nancy), Brendan Hassett (Rice), and Claire Voisin (Paris VI).
• Between October 2003 and October 2005 I organised the Calf (junior COW). For information on current Calf events, please go here. For a historical record of the events I organised, go here.

In the press:

• Math in the Media: A monthly magazine from the AMS
  "Beautiful pictures and animations reminiscent of flowers or folding cloth grace recent posts of this blog, in which most entries take the form of a technical conversation between specialists Tom Coates, Alessio Corti, Sergei Galkin, Vasily Golyshev, and Al Kasprzyk..."
• Physics World: Nature's building blocks brought to life
  "The scientists are looking for shapes, known as "Fano varieties", which are basic building blocks and cannot be broken down into simpler shapes. They find Fano varieties by looking for solutions to a variety of string theory, a theory that seeks to unify quantum mechanics with gravity..."
• Science: Elementary mathematics
  "An international group of mathematicians hopes to do for math what Dmitri Mendeleev’s periodic table did for chemistry by identifying the shapes in three, four, and five dimensions that cannot be divided into other shapes..."
• New Scientist: Atoms ripple in the periodic table of shapes
  "This rippling structure may look like a piece of origami, or an intricate scarf. In fact, it is geometry's answer to the atom because it can't be broken down into smaller components. Inspired by string theory, there is now a way to classify these atoms by their properties – and hunt down their higher dimensional cousins..."
• Cosmos: Mathematicians propose periodic table of shapes
  "Mathematicians have embarked on a three-year project to create their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions..."