Flows, intersections, and stability on hyperbolic arrangements

Lewis, Samuel Carwyn (2024) Flows, intersections, and stability on hyperbolic arrangements. PhD thesis, University of Glasgow.

Abstract

This thesis studies various aspects of stability theory, hyperplane arrangements, and Coxeter combinatorics, often in the hyperbolic setting. We provide a large family of examples of real variation of stability conditions, and fully classify hyperbolic intersection arrangements in dimension two. Our work establishes new connections between generalised Coxeter arrangements and stability conditions for K3 categories. It is motivated by the belief that the hyperbolic (minimally wild) setting is a rich one; combinatorially, representation theoretically, and geometrically, and worthy of further study.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) and the ERC.
• Subjects: H Social Sciences > HA Statistics; Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Funder's Name: Engineering and Physical Sciences Research Council (EPSRC), ERC
• Supervisor's Name: Bellamy, Professor Gwyn and Wemyss, Professor Michael
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84704
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 15 Nov 2024 14:47
• Last Modified: 18 Nov 2024 09:13
• Thesis DOI: 10.5525/gla.thesis.84704
• URI: https://theses.gla.ac.uk/id/eprint/84704