Jonathan Hanke's Website

Research and Software in Number Theory

Individual Mentoring

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Ph.D. Theses

  1. Kate Thompson — Explicit Representation Results for Quadratic Forms over $\mathbb{Q}$ and $\mathbb{Q}(\sqrt{5})$ by Analytic Methods.  (UGA 2008–2014; with secondary advisor Danny Krashen; Thesis)

Masters Theses

  1. Laura Nunley — Geometry of Numbers approach to small solutions to the Extended Legendre equation
    (UGA 2009–2010; secondary advisor to Pete Clark; Thesis)

PROMYS Returning Student Projects

  1. Portfolio Theory
    (PROMYS 2014; Description)
  2. Explicit Reduction theories for binary forms over $\mathbb{Q}(\sqrt{2})$
    (PROMYS 2011; Description)
  3. Conway’s topographs for binary forms over $\mathbb{Q}(\sqrt{2})$
    (PROMYS 2011; Description)
  4. Finiteness Theorems for Binary Hermitian forms over $\mathbb{Z}$
    (PROMYS 2009; Description)
  5. Quaternion arithmetic
    (PROMYS 2008)

Undergraduate Student Theses

  1. Mayank Varia — Explicit calculation of the L-function for Kummer surfaces
    (Duke ????; Thesis with high distinction)
  2. Brandon Levin — ??? Binary Quadratic Forms ???
    (Duke ????; secondary advisor to Les Saper)

Independent Study Courses

  1. Kate Thompson — Quaternion Algebras and Quadratic Forms
    (UGA; Fall 2009, Spring 2010, Fall 2010)
  2. Mandy Frese — Number Theory and Elliptic Curve Cryptography
    (Duke; ????, ????)
  3. Ebony Harvey — Reduction Theories for totally definite Binary Quadratic Forms over $\Bbb{Z}[\sqrt{2}]$
    (Duke; Summer ????)
  4. Mayank Varia
    (Duke; ???? )
  5. Two Crypto people… (Duke; Summer ????) — Combinatorics
  6. Nina & Matt Young VIGRE Reading seminar at Rutgers.

Written by jonhanke

September 15th, 2011 at 7:11 am

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