Now showing items 1-20 of 70

    • 2-Selmer groups and Heegner points on elliptic curves 

      Li, Chao (2015-05-07)
      This thesis studies several aspects of the arithmetic of elliptic curves. In particular, we explore the prediction of the Birch and Swinnerton-Dyer conjecture when the 2-Selmer group has rank one. For certain elliptic ...
    • A p-adic Jacquet-Langlands Correspondence 

      Knight, Erick Phillip (2017-05-16)
      In this paper, we construct a candidate p-adic Jacquet-Langlands correspondence. This is a correspondence between unitary continuous admissible representations of GL2(Qp) valued in p-adic Banach spaces, and unitary continuous ...
    • Algebraicity Criteria and Their Applications 

      Tang, Yunqing (2016-05-04)
      We use generalizations of the Borel–Dwork criterion to prove variants of the Grothedieck–Katz p-curvature conjecture and the conjecture of Ogus for some classes of abelian varieties over number fields. The Grothendieck–Katz ...
    • Algorithms and Models for Genome Biology 

      Zou, James Yang (2014-02-25)
      New advances in genomic technology make it possible to address some of the most fundamental questions in biology for the first time. They also highlight a need for new approaches to analyze and model massive amounts of ...
    • Alternate Compactifications of Hurwitz Spaces 

      Deopurkar, Anand (2012-12-19)
      We construct several modular compactifications of the Hurwitz space \(H^d_{g/h}\) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the ...
    • Anabelian Intersection Theory 

      Silberstein, Aaron (2012-12-19)
      Let F be a field finitely generated and of transcendence degree 2 over \(\bar{\mathbb{Q}}\). We describe a correspondence between the smooth algebraic surfaces X defined over \(\bar{\mathbb{Q}}\) with field of rational ...
    • Analysis of Some PDEs over Manifolds 

      Li, Yi (2013-02-14)
      In this dissertation I discuss and investigate the analytic aspect of several elliptic and parabolic partial differential equations arising from Rimannian and complex geometry, including the generalized Ricci flow, Gaussian ...
    • The Arithmetic of Simple Singularities 

      Thorne, Jack A. (2012-08-10)
      We investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis ...
    • Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds 

      Zhou, Jie (2014-06-06)
      This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of the corresponding topological ...
    • Chiral Principal Series Categories 

      Raskin, Samuel David (2014-06-06)
      This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in the unramified principal series category. ...
    • Complete Homogeneous Varieties via Representation Theory 

      Cavazzani, Francesco (2016-05-02)
      Given an algebraic variety $X\subset\PP^N$ with stabilizer $H$, the quotient $PGL_{N+1}/H$ can be interpreted a parameter space for all $PGL_{N+1}$-translates of $X$. We define $X$ to be a \textit{homogeneous variety} if ...
    • The complex geometry of Teichmüller space 

      Antonakoudis, Stergios M (2014-06-06)
      We study isometric maps between Teichmüller spaces and bounded symmetric domains in their Kobayashi metric. We prove that every totally geodesic isometry from a disk to Teichmüller space is either holomorphic or anti-holomorphic; ...
    • Covers of an Elliptic Curve E and Curves in ExP1 

      Tavares Bujokas, Gabriel (2015-04-30)
      We describe the hyperplane sections of the Severi variety of curves in ExP1 in a similar fashion to Caporaso—Harris’ seminal work. From this description we almost get a recursive formula for the Severi degrees—we get the ...
    • D-Modules on Spaces of Rational Maps and on Other Generic Data 

      Barlev, Jonathan (2012-12-13)
      Fix an algebraic curve X. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined maps from X to a fixed target scheme Y. There are three methods ...
    • Degenerations, Log K3 Pairs and Low Genus Curves on Algebraic Varieties 

      Zahariuc, Adrian Ioan (2016-04-28)
      We investigate several questions pertaining to the enumerative and deformation-theoretic behavior of low-genus curves on algebraic varieties, using specialization techniques.
    • Derived categories and birational geometry of Gushel-Mukai varieties 

      Perry, Alexander Richard (2016-05-17)
      We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether ...
    • The Eigencurve is Proper 

      Diao, Hansheng (2014-06-06)
      Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points correspond to all finite slope overconvergent p-adic eigenforms. We prove the conjecture that the eigencurve Cp,N is proper ...
    • Entire Surfaces of Prescribed Curvature in Minkowski 3-Space 

      Smillie, Peter (2018-05-16)
      This thesis concerns the global theory of properly embedded spacelike surfaces in 3 dimensional Minkowski space with prescribed Gaussian curvature. We prove that every regular domain which is not a wedge contains a unique ...
    • Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems 

      Tiozzo, Giulio (2013-09-30)
      The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued ...
    • Equivariant Weiss Calculus and Loops of Stiefel Manifolds 

      Tynan, Philip Douglas (2016-05-18)
      In the mid 1980s, Steve Mitchell and Bill Richter produced a filtration of the Stiefel manifolds O(V ;W) and U(V ;W) of orthogonal and unitary, respectively, maps V -> V ⊕W stably split as a wedge sum of Thom spaces defined ...