Clyde Kertzer

Research Experience

Developing Inquiry Based Learning (IBL) Presentations, Fall 2024
- Aim: Create interactive talks aimed at undergraduates.
- My talk: Packing Problems & Number Theory
- Here are some laser cut circles associated with the project!
- Advisor: Dr. Emily Montelius
Gallery of Theorems, Spring 2024
- Aim: Represent mathematical concepts using artistic mediums
- Further developed Numberscope visualizer to increase functionality
- Advisor: Professor Sarah Peterson
Independent Study - Parameterizations of Descartes Quadruples, Fall 2023
- Developed honors thesis on Descartes quadruples of Apollonian circle packings
- Advisors: Professor Kate Stange and Professor James Rickards
CU Boulder REU - Apollonian Circle Packings, Summer 2023
- Disproved the Local-Global Conjecture for Apollonian Circle Packings
- Preprint led to an article in Quanta Magazine
- Advisors: Professor Kate Stange and Professor James Rickards
Numberscope - Research Assistant & Developer, Fall 2022
- Programmed visualizer that represents Collatz length of the values of a user-selected sequence from the OEIS using a scaled color gradient and a modular-controlled array.
- Developed the Numberscope website to provide and improve user experience.
- A collage I made using screenshots of my visualizer won the 2023 CU Arts & Sciences art contest!
- Advisor: Professor Kate Stange

Algebraic Number Theory & Reciprocity Laws, Spring 2024
- Reciprocity Laws (Lemmermeyer)
- Advisor: Professor David Grant
Lie Algebras, Spring 2024
- Introduction to Lie Algebras and Representation Theory (Humphreys)
- Advisor: Professor Richard Green
Elliptic Curves, Spring 2023
- Rational Points on Elliptic Curves (Silverman & Tate)
- Advisor: Professor David Grant
Introduction to Number Theory & Quadratic Reciprocity, Fall 2021
- An Introduction to the Theory of Numbers (Niven, Zuckerman, & Montgomery)
- Final presentation slides
- Advisor: Professor Paul Hagelstein