I am a DPhil candidate at the Mathematical Institute in Oxford, under the supervision of Professors Frances Kirwan,
Jason Lotay and Alex Ritter, as well as a member of the MCR of Balliol College. I am being supported by the EPSRC. I was previously an undergraduate
at Oxford, where I completed a Part C dissertation under the supervision of Dr Markus Upmeier and a summer research project under the supervision of Dr Thomas Oliver.
I was also a counsellor for the 2018 edition of PROMYS Europe.

I am interested in moduli problems arising from algebraic geometry, and applying techniques from Geometric Invariant Theory (both reductive and non-reductive) to construct and study moduli spaces.

My email address is cooperg at maths.ox.ac.uk. My CV can be found here.

*Twisting Moduli for \( GL(2) \).*With B. Bedert, T. Oliver and P. Zhang.*Journal of Number Theory*, Volume 217, pp 142-162, December 2020.

arXiv link.

*Moduli Spaces of Hyperplanar Admissible Flags in Projective Space.*arXiv:2304.02453.- This poster was presented at the
*ABGMS*conference.

*GIT Constructions of Compactified Universal Jacobians over Stacks of Stable Maps.*arXiv:2210.11457.- This poster was presented at the
*VBAC 2022*and*BrAG V*conferences.

- I am a co-organiser of the Oxford Junior Geometry seminar alongside Gilles Englebert and Jakub Wiaterek.
**MT 2022:**Reading group on algebraic deformation theory.**TT 2022:**Reading group on Mori dream spaces and GIT.**HT 2022:**Reading group on toric varieties.

**HT 2023:**Tutor for Part B Algebraic Curves.**MT 2022:**Tutor for Part B Geometry of Surfaces and Tutor for Part A Linear Algebra at Wadham College.**TT 2022:**Tutor for Part A Projective Geometry at New College.**HT 2022:**Tutor for Part B Algebraic Curves and TA for Part C Lie Groups.**MT 2021:**Tutor for Prelims Geometry at New College and TA for Part C Algebraic Geometry.**TT 2021:**Tutor for Part A Projective Geometry at New College.**HT 2021:**TA for Part C Lie Groups and Part B Algebraic Curves.**MT 2020:**Tutor for Prelims Geometry at New College.

*Compactified Universal Jacobians over Stacks of Stable Maps via GIT*, Algebraic Geometry Seminar, University of Liverpool, April 2023.*An Introduction to Non-Reductive Geometric Invariant Theory*, Junior Geometry Seminar, University of Oxford, March 2023.*Compactified Universal Jacobians over \( \overline{\mathcal{M}}_{g,n} \) via GIT*, Geometry and Analysis Seminar, University of Oxford, January 2023.*Compactified Universal Jacobians over \( \overline{\mathcal{M}}_{g,n} \) via GIT*, CALF Seminar, University of Cambridge, November 2022.

- VBAC 2023: Recent Applications to the Geometry of Moduli Spaces, Universität Duisburg-Essen, 28 August-1 September 2023.
- Algebraic Groups and their Representations, University of Birmingham, 24-28 July 2023.
- Arithmetic, Birational Geometry and Moduli Spaces, Brown University, 12-16 June 2023.
- Quivers, Clusters, Moduli and Stability, University of Oxford, 9-13 January 2023.
- British Algebraic Geometry Meeting V, Imperial College London, 14-16 September 2022.
- VBAC 2022: Moduli Spaces and Vector Bundles - New Trends, University of Warwick, 25-29 July 2022.
- Conférence à Toulouse pour Simpson (CATS-60), Université de Toulouse III - Paul Sabatier, 20-24 June 2022.
- Summer School on Moduli Spaces and Stability Conditions, Centro Internazionale per la Ricerca Matematica (Trento), 6-10 June 2022.
- Géométrie Algébrique en Liberté XXIX, Université Paris-Saclay, 23-27 May 2022.
- Spring School on Invariants in Algebraic Geometry, Université de Bourgogne, 16-20 May 2022.
- AGGITatE Days, University of Essex, 7-8 April 2022.
- Unifying Themes in Geometry, Lake Como School of Advanced Studies, 27-30 September 2021 (online).
- Summer School on Derived and Triangulated Categories, Bergische Universität Wuppertal, 13-17 September 2021.
- Géométrie Algébrique en Liberté XXVIII, Loughborough University, 5-9 July 2021 (online).
- LMS Undergraduate Summer School, University of Leeds, 14-26 July 2019.
- Various editions of the Junior and Senior COW Seminar.

Here is a collection of various things I've made notes/slides on up to now, mostly for reading groups and seminars that have taken place in Oxford. No claim to originality is made for anything included below, and there (likely) may be mistakes.

- Derived infinity categories of Abelian categories.
- Introduction to deformation theory.
- Functors of Artin rings and Schlessinger's theorem.
- The moduli stack of semistable vector bundles on a smooth projective curve.
- Algebraic stacks and moduli of quiver representations.
- Differentials in algebraic geometry.
- Embedding curves in projective space.
- An introduction to \( n \)-categories.

Office N2.16

Mathematical Institute

Andrew Wiles Building

Woodstock Road

OXFORD

OX2 6GG

United Kingdom

Mathematical Institute

Andrew Wiles Building

Woodstock Road

OXFORD

OX2 6GG

United Kingdom