Browsing Mathematics Theses and Dissertations by Author "Sinha, Dev"

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  • Accessing the Topological Properties of Neural Network Functions. 
    Masden, Marissa (University of Oregon, 2024-01-09)
    We provide a framework for analyzing the geometry and topology of the canonical polyhedral complex of ReLU neural networks, which naturally divides the input space into linear regions. Beginning with a category appropriate ...
  • Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs 
    Chettih, Safia (University of Oregon, 2016-11-21)
    We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit ...
  • Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots 
    Pelatt, Kristine (University of Oregon, 2012)
    We produce explicit geometric representatives of non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live ...
  • Metastable Complex Vector Bundles over Complex Projective Spaces 
    Hu, Yang (University of Oregon, 2024-01-09)
    In the unstable range, topological vector bundles over finite CW complexes are difficult to classify in general. Over complex projective spaces \mathbb{C}P^n, such bundles are far from being fully classified, or even ...
  • The Curtis-Wellington Spectral Sequence Through Cohomology 
    Hunter, Dana (University of Oregon, 2022-10-04)
    We study stable homotopy through unstable methods applied to its representing infinite loop space, as pioneered by Curtis and Wellington. Using cohomology instead of homology, we find a width filtration whose subquotients ...

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