Welcome to my website
Hi, I am Jonathan and welcome to my webpage. I am a mathematician interested in analysis, probability, and combinatorics. My research focuses on applying linear algebra and probability theory to solve combinatorial problems.
I completed my undergraduate studies at Stanford University, where I worked on problems related to minimal and capillary surfaces. I studied how geometric boundary conditions can produce singular behavior in the resulting variational surfaces.
I completed my Master’s degree at Cal State LA, where I conducted research in combinatorics, including work on Cayley graphs, intersecting families, Ramsey Theory on bipartite graphs, and odd cover problems. My Master’s thesis explored extremal graph results on product graphs.
I am currently applying for Mathematics PhD programs.
How to use this site
The Math Notes section provides some of the background on the foundational results and techniques related to my research. In particular, I am currently working on notes for the following topics
- Measure Theory
- Extremal Graph Theory
- Combinatorial Designs
In the future, I plan to add notes for Extremal Set Theory, Graph Limits, Stohastic Processes, Probabilitic Method, Entropy method, and more.
The Teaching section is under construction and will include notes from past classes that I have taught at Cal State LA. I plan to include some class projects created for students to explore applications of mathematics to biology, chemistry, and economics. I also plan to include some interactive content to allow K-12 students to explore open math problems.
The Research section contains some background on research problems that I have studied in the past and that I plan to pursue in the future. Currently, I have some content on Modtown problems. I plan to add content related to odd representations of hypergraphs, algebraic Unit Distance graphs, Sunflower Conjecture variants, EKR Theory of Triangulations, flag algebras on Hamming graphs, and refined absorption.
The Demos section of my webpage is dedicated to interactive visualizations and simulations of some interesting random geometric and/or combinatorial objects. I often use the simulations while giving talks in outreach programs or seminars. Feel free to use or share these simulations with others. (Disclaimer: I am a mathematician not a programmer. I have used AI to assist me in writing the Javascript simulations. I have looked over the code myself, but I cannot guarantee there are no bugs.)
Contact
Email: jonathan.j.davidson@gmail.com
Github: jjdavidson