Now showing items 1-8 of 8

    • A Functorial Approach to Algebraic Vision 

      Van Meter, Lucas
      We study multiview moduli problems that arise in computer vision. We show that these moduli spaces are always smooth and irreducible, in both the calibrated and uncalibrated cases, for any number of views. We also show ...
    • Arithmetic Properties of the Derived Category for Calabi-Yau Varieties 

      Ward, Matthew J
      This thesis develops a theory of arithmetic Fourier-Mukai transforms in order to obtain results about equivalences between the derived category of Calabi-Yau varieties over non-algebraically closed fields. We obtain answers ...
    • Bispectral Operator Algebras 

      Casper, William Riley
      This dissertation is an amalgamation of various results on the structure of bispectral differential operator algebras, ie. algebras of differential operators with possibly noncommutative coefficients in a variable $x$ ...
    • Deformations of Categories of Coherent Sheaves and Fourier-Mukai Transforms 

      Grigg, Nathan (2013-07-25)
      In modern algebraic geometry, an algebraic variety is often studied by way of its category of coherent sheaves or derived category. Recent work by Toda has shown that infinitesimal deformations of the category of coherent ...
    • Projective Geometry for Perfectoid Spaces 

      Dorfsman-Hopkins, Gabriel David
      To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a ...
    • Some Theorems on the Resolution Property and the Brauer map 

      Mathur, Siddharth
      Using formal-local methods, we prove that a separated and normal Deligne-Mumford surface must satisfy the resolution property, this includes the first class of separated algebraic spaces which are not schemes. Our analysis ...
    • Toward the compactification of the stack of Lie(G)-forms using perfect complexes 

      Zsamboki, Pal
      To establish geometric properties of an algebraic stack, one can find a compactification. This method has been successfully employed to find irreducible components for example of the moduli stack of curves [DM69], vector ...
    • Twistor Spaces for Supersingular K3 Surfaces 

      Bragg, Daniel
      We develop a theory of twistor spaces for supersingular K3 surfaces, extending Artin's analogy between supersingular K3 surfaces and complex analytic K3 surfaces. Our twistor spaces are families of twisted supersingular ...