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Browsing by Author "Heineman, Kristin, committee member"

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    How to prioritize as a citizen of the universe
    (Colorado State University. Libraries, 2024) Colter, Jackson T., author; Kasser, Jeff, advisor; Archie, Andre, committee member; Heineman, Kristin, committee member
    Stoicism has gained a bit of popularity in certain circles recently, and much of this popularity revolves around the way that Stoicism enables and guides moral progress on an individual level, regardless of the circumstances. However, Stoic ethics also features an element of cosmopolitanism - essentially, other-oriented ethical principles that an ideal Stoic would follow. These principles tell us that we are all members of a common rational community, with every agent in the rationally organized universe being a member of this community. Naturally, the human lifespan is not long enough to equally address every rational being in the universe, so some sort of prioritization is required. However, Stoics place two requirements on our actions. We must ground our actions in knowledge, and both Marcus Aurelius and Epictetus directly advise us to avoid unnecessary actions. These requirements combined with the other-oriented moral principles lead Stoics to a state of moral paralysis - where the actions that seem to be morally required of them are epistemically unjustified. This paralysis needs to be solved if Stoicism is to serve as a meaningful system of other-oriented ethics. Fortunately, an account of expertise is given in a piece of secondary literature by Simon Shogry which, combined with later Stoic insights, serves to alleviate this paralysis.
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    Properties of tautological classes and their intersections
    (Colorado State University. Libraries, 2019) Blankers, Vance T., author; Cavalieri, Renzo, advisor; Achter, Jeff, committee member; Pries, Rachel, committee member; Shoemaker, Mark, committee member; Heineman, Kristin, committee member
    The tautological ring of the moduli space of curves is an object of interest to algebraic geometers in Gromov-Witten theory and enumerative geometry more broadly. The intersection theory of this ring has a highly combinatorial structure, and we develop and exploit this structure for several ends. First, in Chapter 2 we show that hyperelliptic loci are rigid and extremal in the cone of effective classes on the moduli space of curves in genus two, while establishing the skeleton for similar results in higher genus. In Chapter 3 we connect the intersection theory of three families of important tautological classes (Ψ-, ω-, and κ-classes) at both the cycle and numerical level. We also show Witten's conjecture holds for κ-classes and reformulate the Virasoro operators in terms of κ-classes, allowing us to effectively compute relations in the κ-class subring. Finally, in Chapter 4 we generalize the results of the previous chapter to weighted Ψ-classes on Hassett spaces.