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Showing 1 to 6 of 6 for “"Incidence geometry"”.
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Semi-algebraic graphs and hypergraphs in incidence geometry
… this dissertation, we discuss three problems in incidence geometry where the bounds for semi-algebraic (hyper)graphs are generally better than the ones for arbitrary (hyper)graphs : (1) what is the maximum number of hyperedges in a hypergraph forbidding some pattern? (2) what is the most compact …
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Incidence geometry from an algebraic graph theory point of view
… techniques from algebraic graph theory to finite incidence geometry. The incidence geometries under consideration include projective spaces, polar spaces and near polygons. These geometries give rise to one or more graphs. By use of eigenvalue techniques, we obtain results on these graphs and on …
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Polynomial partitioning and incidence problems in higher dimensions
Incidence geometry is the study of the intersection patterns of simple geometric objects. One of the breakthroughs in this field is the polynomial partitioning technique introduced by Guth and Katz. In this thesis, I will present two results on incidence problems with high-dimensional objects: an …
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Additive stucture, rich lines, and exponential set-expansion
… The second result will establish a new tool in incidence geometry, which should prove useful in attacking combinatorial estimates. The third result evolved from the famous sum-product problem, by providing a partial categorization of bivariate polynomial set functions which induce exponential …
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Reducibility and Statistical-Computational Gaps from Secret Leakage
… to combinatorial designs based on the incidence geometry of Fᵗᵣ and to random matrix theory. In particular, we show a convergence result between Wishart and inverse Wishart matrices that may be of independent interest. The specific hardness conjectures for PCₚ implying our …
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Resolution and Coherence Length at a Pulsed Neutron Reflectometer
Made available in DSpace on 2017-07-06T18:55:28Z (GMT). No. of bitstreams: 3 Munter_Alan_E_MS.pdf: 40474809 bytes, checksum: f2e28c39fc5abcce0b18692a47c9824b (MD5) Munter_Alan_E_MS_ABS.pdf: 1029800 bytes, checksum: e2d468ba1ac6fcf8ef50b822d99e2b5f (MD5) license.txt: 4813 bytes, checksum: …