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Recent Submissions

  • On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication 

    Kezuka, Yukako (2017-05-30)
    The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, ...
  • Exploring Random Geometry with the Gaussian Free Field 

    Jackson, Henry Richard (2016-10-01)
    This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum. Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, ...
  • On a Heegaard Floer theory for tangles 

    Zibrowius, CB (2017-03-10)
    The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification ...
  • $\textit{K}$-Theory of Fermat Curves 

    Cain, Christopher (Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 2017-01-10)
    I investigate the $K_2$ groups of the quotients of Fermat curves given in projective coordinates by the equation $F_n:X^n+Y^n=Z^n$. On any quotient where the number of known elements is equal to the rank predicted by ...

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