Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 6 of 6 for “"geometry-of-numbers"”.
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Arithmetic statistics and Vinberg representations
… statistics through Vinberg representations. Very often, the rational and integral orbits of Vinberg representations encode information about certain arithmetic objects of interest. In view of that, we can use Bhargava's techniques in geometry-of-numbers to count these orbits and prove results on …
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
… laced Dynkin diagram gives rise to a family of curves over Q and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a strong link between the arithmetic of these curves and the rational orbits of …
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Lattice Extensions and Zeros of Multilinear Polynomials
… treat several problems related to the existence of lattice extensions preserving certain geometric properties and small-height zeros of various multilinear polynomials. An extension of a Euclidean lattice $L_1$ is a lattice $L_2$ of higher rank containing $L_1$ so that the intersection of $L_2$ …
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions
In this thesis, we examine theoretical aspects of the Gomory-Chvátal closure of polyhedra. A Gomory-Chvátal cutting plane for a polyhedron P is derived from any rational inequality that is valid for P by shifting the boundary of the associated half-space towards the polyhedron until it intersects …
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Diophantine Avoidance, Number Fields, and Quadratic Forms
… term refers to effective results on existence of points of bounded size (where size is measured by norm or height, depending on the context) in a given algebraic set avoiding some specified subsets. The application of avoidance conditions allows to understand how ``well distributed" are points …
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Capitulation Discriminants of Genus One Curves
In this thesis we study genus one curves of degree n embedded in projective space P n−1 . We are speci cally interested in the curves de ned over Q that are counterexamples to the Hasse principle, that is the curves that have points everywhere locally but no Q-points. These curves correspond to …