Calum Crossley
- Location: University College London
- E-mail: calum dot crossley dot 23 @ucl.ac.uk
- CV: cv.pdf
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. More specifically, I have been using matrix factorizations to study categorical resolutions.
Papers and Preprints
- (ii) Odd Knörrer periodicity as a double cover.
- (i) A categorical flop in dimension one Forum Math. Sigma (2026).
Talks
- 'Matrix factorizations, odd gradings and double covers' for MAGIC, 01 June 2026.
- 'Gluing curves and quivers' at Calf, 20 March 2026.
- 'Guide to Orlov's theorem' for DOGS (notes), 25 November 2025.
- 'Categorical resolutions from geometry' for DANCE (notes, video), 3 November 2025.
- 'Crepancy of categorical resolutions' for MAGIC, 23 June 2025.
- 'Quivers and Koszul duality' for the Imperial Derived Categories Seminar (notes), 10 March 2025.
- 'Matrix factorizations and Knörrer periodicity' for the KCL / UCL Junior Geometry Seminar (notes), 20 January 2025.
- 'Matrix factorizations and Knörrer periodicity' for DOGS (notes), 14 January 2025.
- 'Cohomology and derived categories' for the Imperial Junior Geometry Seminar, 4 October 2024.
Travels
- Oxford Algebraic Geometry Days, Oxford, September 2026.
- Symplectic geometry workshop, St Andrews, July 2026.
- LMS-Sheffield, Sheffield, July 2026.
- RGAS summer school, Zaragoza, June 2026.
- GAP XX, Kyoto, April 2026.
- Workshop on homological algebra, Salerno, March 2026.
- FanoHK, Toulouse, December 2025.
- CAGE, Leiden, September 2025.
- BrAG VII, Nottingham, September 2025.
- Workshop on derived categories, Cetraro, July 2025.
- GLEN, Sheffield, April 2025.
- Mirrors in the Midlands, Birmingham, August 2024.
Organization
- DOGS (Derived Obsessed Graduate Students), 2025-2026.
- KCL / UCL Junior Geometry Seminar, 2024-2025.
Teaching
- Algebra 2 (UCL), TA, Spring 2026.
- Algebra 3 (UCL), TA, Autumn 2025.
- Advanced Linear Algebra (UCL), Marker, Spring 2025.
- Effective Methods in Algebra (LMO), TA, Spring 2025.
- Algebra 1 (UCL), TA, Autumn 2024.
- Foundations and Proofs (UCL), Marker, Autumn 2024.