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I am a fourth year PhD student in mathematics at the University of Edinburgh. My supervisor is Prof. Arend Bayer. I am a member of the School of Mathematics, as well as the Hodge Institute.

From September 2024 I'll be a postdoc in the Mathematical Institute at the University of Bonn, in the working group of Daniel Huybrechts.

Email: h (dot) dell (at) sms (dot) ed (dot) ac (dot) uk

Address: Room 5210, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD

Pronouns: she/they

Research Interests

I am interested in algebraic geometry, in particular derived categories of coherent sheaves, Bridgeland stability conditions, and group actions (on varieties and categories).

In my first project, I studied the stability manifold of (smooth projective) surfaces which are free abelian quotients. One approach is via group actions on triangulated categories, another is via Le Potier functions:

  • Stability Conditions on Free Abelian Quotients, arXiv.

I am also thinking about derived categories of cyclic covers, and the question of whether such a cover can be recovered (up to isomorphism) from its Kuznetsov component:

  • Cyclic covers: Hodge theory and categorical Torelli theorems, joint with Augustinas Jacovskis and Franco Rota, arXiv.

I have also been investigating how stability conditions behave under actions of fusion categories (=tensor categories with extra structure). A crucial example is that, if a finite group G acts on a category D, then the corresponding G-equivariant category is a module category over Rep(G) (which is a fusion category). As an application, we generalise a result from my first project to non abelian groups.

  • Fusion-equivariant stability conditions and Morita duality, joint with Edmund Heng and Anthony Licata, arXiv.

Background

Before coming to Edinburgh, I did an integrated masters degree at the University of Warwick.

Other Activities

I previously organised GAeL XXX (University of Warwick, July 2023) and GAeL XXIX (Université Paris-Saclay, May 2022).

I co-organise the Edinburgh Geometry seminar (EDGE).

I regularly attend the CALF, GEARS, and GLEN seminars.

When I'm not doing maths, I like to hike, climb, and kayak.