PDF’s

Here are some of the documents I have written, along with brief summaries of what they contain.

LSGNT:

NCCR for the affine cone of the Grassmannian - Using the framework that Spenko-Van den Bergh provides, we find a NCCR for the affine cone of the Grassmannian, Hom(C^n,C^k)/SL(k). We then relate it to a categorical resolution, and prove that two different NCCR’s are derived equivalent.

Non Commutative Crepant Resolutions - First LSGNT mini project, with Ed Segal - A brief introduction to non-commuative crepant resolutions, mainly based on Spenko - Van den Bergh: Non-commuative resolutions of quotient singularites, written with the aim of explaining the key ideas, focusing on the simpler case of torus actions.

Moduli Space of Stable Maps - Second LSGNT Mini project, with Cristina Manolache - Proves the existence of the Hilbert scheme and uses that to give a sketch construction on the Moduli space of stable maps of genus g. Introduces Gromov-Witten invaraints for projective space and proves a recursion formula for degree d rational curves, also contains code to calculate GW invariants for projective space.

Older stuff from my Undergraduate:

An Introduction to Hochschild (co)homology - 4th year project at Imperial, with Ed Segal - An introduction to Hochschild (co)homology, including Morita invariance and interpretation as deformations.

Finite projective planes - 2nd year group project at Imperial, is an introduction to finite projective planes and finite fields.