# Soren Gammelgaard

DPhil Student

**Address**

Mathematical Institute

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

Papers:**Punctual Hilbert schemes for Kleinian singularities as quiver varieties**

*Craw, A; Gammelgaard, S; Gyenge, Á; Szendrői, B*Algebraic Geometry 8 (6) (2021) 680–704**Quot schemes for Kleinian orbifolds Craw, A; Gammelgaard, S; Gyenge, Á; Szendrői, B**

Symmetry, Integrability and Geometry: Methods and Applications SIGMA 17 (2021)

MT18, MT19: TA in Galois Theory

HT20: TA in Commutative Algebra, Tutor in Topology, St Peter's College

HT21: TA in Algebraic Curves

MT21: TA in Homological Algebra

HT22: Tutor in Algebraic Curves

I am interested in moduli spaces attached to the action of finite groups on affine spaces, and their connections with quiver varieties.

For instance, we can let G be a finite subgroup of $ SL_2(\mathbb C)$: then we can consider the symmetric powers of the singularity $X=\mathbb C^2/G$, the punctual Hilbert schemes $\operatorname{Hilb}^n X$, or the same constructions with the minimal resolution of X in its place. Generalising, we can also consider spaces of torsion-free sheaves on these singularities or their resolutions - to make the theory work well, it usually becomes necessary to compactify these singularities, for instance as Deligne-Mumford stacks.

Many of these spaces can be constructed as quiver varieties, which is the focus of my research.

For more details on my current and future research, please see https://sorengam.github.io/research_detailed.

I am also interested in:

- Grothendieck rings of varieties
- Hodge Theory
- Fano schemes and cubic hypersurfaces (this was the subject of my master's thesis).