DAISEY, OLIVER,JAMES (2025) Tropical Homotopy Continuation and Laurent Phenomenon Algebras. Doctoral thesis, Durham University.
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Abstract
Tropical geometry and the theory of Laurent phenomenon algebras (LPAs) both provide powerful frameworks for understanding algebro geometric objects in both pure and applied contexts. This thesis explores both of these topics. We extend Anders Jensen's technique of tropical homotopy continuation for computing stable intersections to the setting of Bergman fans, with applications to chemical reaction network theory and rigidity theory. On the other hand, we investigate the structure of LPAs arising from the configurations of lines on del Pezzo surfaces and explicitly describe a new finite-type LPA cluster structure on the homogeneous coordinate ring of the Cayley plane.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Award: | Doctor of Philosophy |
| Keywords: | algebraic geometry; tropical geometry; computational algebraic geometry; cluster algebras; laurent phenomenon algebras; polyhedral geometry; julia; chemical reaction networks; rigidity theory; homogeneous spaces; del Pezzo surfaces; cayley plane; freudenthal variety; exchange graph |
| Faculty and Department: | Faculty of Science > Mathematical Sciences, Department of |
| Thesis Date: | 2025 |
| Copyright: | Copyright of this thesis is held by the author |
| Deposited On: | 17 Jun 2025 09:46 |
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