Welcome

I am a mathematician interested in analysis and combinatorics, with a focus on problems where discrete structure gives rise to analytic phenomena. I am particularly motivated by questions of convergence: when do large finite objects admit meaningful continuum limits, and what analytic tools are required to understand them?

I am currently studying the theory of large networks and graph limits as a toy model for this transition. Ultimately, I aim to solve discrete optimization problems via analytic methods applied to the corresponding limiting combinatorial objects.

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Background

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:

• The chromatic number of abelian Cayley graphs
• The multicolored Erdős box problem
• Extremal graph theory

My Master’s thesis explored topics in the extremal theory of product graphs. In my study of extremal graph theory, I encountered the ideas of flag algebras and graph limits, and I decided to start exploring more analytical approaches to extremal combinatorics.

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Contact

Email: jonathan.j.davidson@gmail.com