Now showing items 1-20 of 89

    • 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 Model 2-Category of Enriched Combinatorial Premodel Categories 

      Barton, Reid William (2019-09-10)
      Quillen equivalences induce equivalences of homotopy theories and therefore form a natural choice for the "weak equivalences" between model categories. In [21], Hovey asked whether the 2-category Mod of model categories ...
    • 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 ...
    • Applications of Combinatorics to Problems of Geometry 

      Spink, Hunter (2020-05-06)
      This thesis concerns applications of combinatorics to problems of geometry. Combinatorics and geometry are almost antipodal in the world of mathematics. Through the lens of combinatorics, mathematics is discrete and finitary, ...
    • Applications of Equivariant Cohomology to Enumerative Geometry 

      Tseng, Dennis (2020-04-30)
      We show how equivariant cohomology can be applied to enumerative geometry in three different settings: orbits of plane curves, strata of points on a line, and effective divisors on the moduli space of curves. We first give ...
    • 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 ...
    • Asymptotic Phenomena in the Six-Vertex Model 

      Aggarwal, Amol (2020-04-29)
      In this thesis we establish several results concerning the large scale geometry of six-vertex models. These include limit shape phenomena, fluctuation theorems, convergence of local statistics, and boundary-induced phase ...
    • 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 ...