Calum Crossley
- Location: University College London
- E-mail: calum dot crossley dot 23 @ucl.ac.uk
- CV: cv.pdf (updated 2024)
About
Hello! I'm Calum Crossley, currently a PhD student in mathematics at UCL as part of the LSGNT, supervised by Ed Segal.
My research is within algebraic geometry, working with derived categories of sheaves on varieties. I am also interested in matrix factorizations of polynomials, which give a deformed version of these derived categories relating to the physics-inspired conjectures of homological mirror symmetry.
I've been a student with the LSGNT since Autumn 2023. As an undergraduate, I completed an MMath degree at the University of Oxford during 2019-2023, with a masters' thesis on varieties over finite fields supervised by Alan Lauder.
Preprints
- (2025) ' A categorical flop in dimension one'.
Talks and Seminars
I am currently co-organizing the KCL / UCL Junior Geometry Seminar for 2024-2025.
Talks:
- 23 Jun 2025, 'Crepancy of categorical resolutions' for the MAGIC Seminar.
- 10 Mar 2025, 'Quivers and Koszul duality' for the Imperial Derived Categories Seminar (notes).
- 20 Jan 2025, 'Matrix factorizations and Knörrer periodicity' for the KCL / UCL Junior Geometry Seminar (notes).
- 14 Jan 2025, 'Matrix factorizations and Knörrer periodicity' for DOGS (notes).
- 4 Oct 2024, 'Cohomology and derived categories' for the Imperial Junior Geometry Seminar.
Teaching
- Spring 2025: Advanced Linear Algebra (UCL), Marker.
- Spring 2025: Effective Methods in Algebra (LMO), TA.
- Autumn 2024: Algebra 1 (UCL), TA.
- Autumn 2024: Foundations and Proofs (UCL), Marker.
Notes
Be warned, these may contain errors:- Derived categories mini-project with Bogdan Simeonov and Ines Chung-Halpern, supervised by Ed Segal, 2023-2024.
- LSGNT 'Elliptic Curves' by Vladimir Dokchitser, personal notes from 2023-2024.
- LSGNT 'Topics in Geometry', personal notes from 2023-2024.
- LTCC 'Birational Geometry' by Calum Spicer, personal notes from 2023-2024.