Calum Crossley

Location: University College London
E-mail: calum dot crossley dot 23 @ucl.ac.uk
CV: cv.pdf (updated 2024)
Github: https://github.com/CalumCrossley

About

I'm Calum Crossley, currently a PhD student in mathematics at UCL as part of the LSGNT, supervised by Ed Segal.

I study algebraic geometry using homological algebra, in the guise of derived categories of sheaves. 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.

Education

I have 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.

Talks and Seminars

I am currently co-organizing the KCL / UCL Junior Geometry Seminar for 2024-2025.

Talks:

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: Effective Methods in Algebra (LMO), Assistant.
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 Geometry Topics, personal notes from 2023-2024.
LTCC Birational Geometry by Calum Spicer, personal notes from 2023-2024.