Jonathan Hanke's Website

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.