## Individual Mentoring

[latexpage]

**Ph.D. Theses**

**Ph.D. Theses**

- 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**

**Masters Theses**

- 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**

**PROMYS Returning Student Projects**

- Portfolio Theory

(PROMYS 2014; Description) - Explicit Reduction theories for binary forms over $\mathbb{Q}(\sqrt{2})$

(PROMYS 2011; Description) - Conway’s topographs for binary forms over $\mathbb{Q}(\sqrt{2})$

(PROMYS 2011; Description) - Finiteness Theorems for Binary Hermitian forms over $\mathbb{Z}$

(PROMYS 2009; Description) - Quaternion arithmetic

(PROMYS 2008)

**Undergraduate Student Theses**

**Undergraduate Student Theses**

- Mayank Varia — Explicit calculation of the L-function for Kummer surfaces

(Duke ????; Thesis with high distinction) - Brandon Levin — ??? Binary Quadratic Forms ???

(Duke ????; secondary advisor to Les Saper)

**Independent Study Courses**

**Independent Study Courses**

- Kate Thompson — Quaternion Algebras and Quadratic Forms

(UGA; Fall 2009, Spring 2010, Fall 2010) - Mandy Frese — Number Theory and Elliptic Curve Cryptography

(Duke; ????, ????) - Ebony Harvey — Reduction Theories for totally definite Binary Quadratic Forms over $\Bbb{Z}[\sqrt{2}]$

(Duke; Summer ????) - Mayank Varia —

(Duke; ???? ) - Two Crypto people… (Duke; Summer ????) — Combinatorics
- Nina & Matt Young VIGRE Reading seminar at Rutgers.