Browsing by Author "Tucker, Dustin, committee member"
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Item Open Access Defining persistence diagrams for cohomology of a cofiltration indexed over a finite lattice(Colorado State University. Libraries, 2022) Rask, Tatum D., author; Patel, Amit, advisor; Shoemaker, Mark, committee member; Tucker, Dustin, committee memberPersistent homology and cohomology are important tools in topological data analysis, allowing us to track how homological features change as we move through a filtration of a space. Original work in the area focused on filtrations indexed over a totally ordered set, but more recent work has been done to generalize persistent homology. In one avenue of generalization, McCleary and Patel prove functoriality and stability of persistent homology of a filtration indexed over any finite lattice. In this thesis, we show a similar result for persistent cohomology of a cofiltration. That is, for P a finite lattice and F : P → ▽K a cofiltration, the nth persistence diagram is defined as the Möbius inversion of the nth birth-death function. We show that, much like in the setting of persistent homology of a filtration, this composition is functorial and stable with respect to the edit distance. With a general definition of persistent cohomology, we hope to discover whether duality theorems from 1-parameter persistence generalize to more general lattices.Item Open Access Pseudostable Hodge classes(Colorado State University. Libraries, 2024) Williams, Matthew M., author; Cavalieri, Renzo, advisor; Gillespie, Maria, committee member; Peterson, Chris, committee member; Tucker, Dustin, committee memberWe study the relationship between Hodge classes on moduli spaces of pseudostable and stable curves given by the contraction morphism T. While Mumford's relation does not hold in the pseudostable case, we show that one can express the (pullback via T of the) Chern classes of E ⊕ E^∨ solely in terms of strata and ψ classes. We organize the combinatorial structure of the pullback of products of two pseudostable λ classes and obtain an explicit comparison of arbitrary pseudostable and stable quadratic Hodge integrals, as well as certain families of cubic and higher degree pseudostable Hodge integrals.Item Open Access The ethical hunter: how to consume animal life(Colorado State University. Libraries, 2013) Flygt, Adrian A., author; Rollin, Bernard E., advisor; Tucker, Dustin, committee member; Callahan, Gerald, committee memberTo view the abstract, please see the full text of the document.Item Open Access Upayā-kauśala as the pragmatic justification of Madhyamaka ethical claims(Colorado State University. Libraries, 2018) Quist, Andrew, author; MacKenzie, Matthew, advisor; Tucker, Dustin, committee member; Hickey, Matthew, committee memberMadhyamaka Buddhism is typically characterized as a particularly thoroughgoing form of anti-foundationalism. This leads to difficulties when trying to justify knowledge claims as well as ethical claims, especially in the light of how these claims are handled in mainstream Abhidharma Buddhism. The ethical domain is particularly important for Buddhism since the Buddhist project is fundamentally soteriological. I endeavor to offer a plausible way that truth claims, especially ethical truth claims, can be justified while keeping to Madhyamaka's metaphysical commitments. Specifically, I will argue that a functional-pragmatist approach – I use the term upāya-kauśalya or "skillful means" – is the most promising way that Madhyamaka can situate the normativity of ethical claims.