Gavin Brown
 |
Gavin BrownProfessor of Mathematics Office: D2.07 Homepage: |
Open Day talks: the taster lecture is linked hereLink opens in a new window, and the exercises are hereLink opens in a new window.
Teaching Responsibilities:
Term 2: MA150 Algebra 2Link opens in a new window.
Previous lecture notes are linked hereLink opens in a new window, in case you'd like to look ahead. (The notes may seem long, but they review a lot of things you already know, and the lectures will focus on the new ideas. You probably know a lot of Part I. Part II is the main new theory. Part III works through eigenvectors, which you may already have some feeling for.)
Research Interests:
Birational classification in algebraic geometry, including computer-assisted constructions and databases.
Some recent publications:
- Local normal forms of noncommutative functions, with M. Wemyss,
Forum of Mathematics, Pi (2025), Vol. 13:e8 1-59. (, arXiv: ) - Derived deformation theory of crepant curves, with M. Wemyss.
Journal of Topology (2024) 42pp. (DOI:; arXiv: ) - Extending Tom and Jerry for Fano 3-folds, with S. Coughlan and T. Ducat, ZAG Handbook of Modern Algebraic Geometry (2025) 5pp. (preprint)
- Noncommutative Singularity Theory, with M. Wemyss,
EMS Surv. Math. Sci. (2024) 20pp. (arXiv: ) -
Kawamata boundedness for Fano threefolds and the Graded Ring Database, with A.M. Kasprzyk, (2022) 23pp. (Available at arXiv: )
- Gorenstein Formats, Canonical and Calabi–Yau Threefolds, with Alexander Kasprzyk and Lei Zhu.
Exp. Math. 31 (2022) 146-164. () -
Recent Developments in Algebraic Geometry -- to Miles Reid for his 70th birthday. Edited with Hamid Abban, Alexander Kasprzyk, Shigefumi Mori.
London Math. Soc. Lecture Note Series 478. CUP 2022, x+356pp. [ISBN: 978-1-009-18085-6] () - Tutorial on Tom and Jerry: the two smoothings of the anticanonical cone over P(1,2,3), with Miles Reid and Jan Stevens.
EMS Surv. Math. Sci 8 (2021) 25-38. (arXiv: ) -
Hodge numbers and deformations of Fano 3-folds, with Enrico Fatighenti.
Documenta Math. 25 (2020) 267-308. ()
-
Gopakumar–Vafa invariants do not determine flops, with Michael Wemyss,
Commun. Math. Phys. 361 (2018) 143–154. ( -
Fano 3-folds in P2 脳 P2 format, Tom and Jerry, with A.M. Kasprzyk and M.I. Qureshi,
Eur. J. Math. 4 (Edge volume) (2018) 51–72. (arXiv: ) -
Polarized Calabi–Yau 3-folds in codimension 4, with Konstantinos Georgiadis,
Mathematische Nachrichten 290:5–6 (2017), 710–725. -
Diptych varieties. II, Apolar varieties, with Miles Reid,
Higher Dimensional Algebraic Geometry, Adv. Stud. in Pure Math. 74 (2017), 41–72. -
Four-dimensional projective orbifold hypersurfaces, with A. Kasprzyk,
Experimental Mathematics 25:2 (2016), 176–193. -
Diptych varieties. I, with Miles Reid,
Proc. London Math. Soc (3) 107 (2013), 1353–1394.