Calum Crossley

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. More specifically, I have been using matrix factorizations to study categorical resolutions.

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.

Preprints

• (2025) ' A categorical flop in dimension one'.

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.

Organization

• (2024-2025) Co-organized the KCL / UCL Junior Geometry Seminar.

Seminar Recommendations

• Online: DOGS, DANCE, SMS.
• London: G&T, MAGIC, Imperial Junior Geometry, CAG@QMUL.
• UK: COW, CALF, GLEN, BrAG.

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.

Old LSGNT 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.