Browsing Student Works by Author "Proudfoot, Nicholas"

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  • Abelian Arrangements 
    Bibby, Christin (University of Oregon, 2015-08-18)
    An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement ...
  • Categorical Invariants of Graphs and Matroids 
    Miyata, Dane (University of Oregon, 2024-01-09)
    Graphs and matroids are two of the most important objects in combinatorics.We study invariants of graphs and matroids that behave well with respect to certain morphisms by realizing these invariants as functors from a ...
  • Faithful tropicalization of hypertoric varieties 
    Kutler, Max (University of Oregon, 2017-09-06)
    The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral ...
  • GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O 
    Hilburn, Justin (University of Oregon, 2016-10-27)
    In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Ka ...
  • Group Actions on Hyperplane Arrangements 
    Moseley, Daniel (University of Oregon, 2012)
    In this dissertation, we will look at two families of algebras with connections to hyperplane arrangements that admit actions of finite groups. One of the fundamental questions to ask is how these decompose into irreducible ...
  • Kazhdan-Lusztig Polynomials of Matroids and Their Roots 
    Gedeon, Katie (University of Oregon, 2018-10-31)
    The Kazhdan-Lusztig polynomial of a matroid M, denoted P_M( t ), was recently defined by Elias, Proudfoot, and Wakefield. These polynomials are analogous to the classical Kazhdan-Lusztig polynomials associated with Coxeter ...
  • NC-algebroid thickenings of moduli spaces and bimodule extensions of vector bundles over NC-smooth schemes 
    Dyer, Ben (University of Oregon, 2018-04-10)
    We begin by reviewing the theory of NC-schemes and NC-smoothness, as introduced by Kapranov in \cite{Kapranov} and developed further by Polishchuk and Tu in \cite{PT}. For a smooth algebraic variety $X$ with a ...
  • Zonotopes and Hypertoric Varieties 
    Arbo, Matthew (University of Oregon, 2016-02-23)
    Hypertoric varieties are a class of conical symplectic resolutions which are very computable. In the current literature, they are only defined constructively, using hyperplane arrangements. We provide an abstract ...

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