Browsing Theses & Dissertations by Author "Addington, Nicolas"

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  • A Categorical sl_2 Action on Some Moduli Spaces of Sheaves 
    Takahashi, Ryan (University of Oregon, 2020-09-24)
    We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, ...
  • Information and Interaction: On the Specialization of General System Theory 
    Vischer, Alexander (University of Oregon, 2021)
    In the natural sciences, there is a prevalent structure: a structure that involves things that interact with each other through time. In classical physics, there is a theory that describes this structure and that is Newtonian ...
  • Lines on Cubic Threefolds and Fourfolds Containing a Plane 
    Brooke, Corey (University of Oregon, 2024-01-09)
    This thesis describes the Fano scheme $F(Y)$ of lines on a general cubic threefold $Y$ containing a plane over a field $k$ of characteristic different from $2$. One irreducible component of $F(Y)$ is birational (over $k$) ...
  • Moduli Spaces of Hermite-Einstein Connections over K3 Surfaces 
    Wray, Andrew (University of Oregon, 2020-09-24)
    We study the moduli space M of twisted Hermite-Einstein connections on a vector bundle over a K3 surface X. We show that the universal bundle can be viewed as a family of stable vector bundles over M parameterized by X, ...
  • Moduli Spaces of Sheaves on K3 Surfaces and Galois Representations 
    Frei, Sarah (University of Oregon, 2019-09-18)
    We consider two K3 surfaces defined over an arbitrary field, together with a smooth proper moduli space of stable sheaves on each. When the moduli spaces have the same dimension, we prove that if the etale cohomology groups ...

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