Asymptotic phenomena through the lens of topological noetherianity

This thesis examines universality and topological Noetherianity in asymptotic algebra, focusing on the behavior of geometric and algebraic structures in large contexts to simplify infinite problems. The first section explores the universality of maximal isotropic Grassmannians in quadratic spaces, building on the work of Kasman et al. It demonstrates that these Grassmannians can be defined set-theoretically by pulling back equations from lower-dimensional Grassmannians through specific maps. The second section addresses topological Noetherianity in infinite-dimensional spaces, inspired by Draisma-Eggermont. It establishes topological Noetherianity for infinite half-spin representations linked to isotropic Grassmannians, introducing half-spin varieties and exploring their applications. The final section extends the study to symplectic spaces, focusing on Noetherianity and universality for Lagrangian Plücker varieties. It examines Lagrangian Grassmann cones and LGCP maps, proving universality for the Lagrangian Grassmannian GrL(4). Additionally, it shows that the dual of ker∞ is topologically Sp(V∞)-Noetherian, where Sp(V∞) denotes the infinite symplectic group.

2024

dissertation

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