Hey, I'm Jasmine Burns.

Pardon the paywalled previous posts. Some of what’s here began as sketches—notes, fragments, and speculative essays that later grew into research papers. They capture ideas in motion rather than finished work.

Anyway...

I'm a graduate student at Virgina Tech. My research began in algebraic topology, shifted to differential geometry, fumbled through category theory, formalized through ergodic theory (PhD pending...) and currently orbits analytic number theory. I wasn't too fond of analysis or number theory as a young mathematician; I mainly wanted to study geometry/topology. I enjoy studying shapes. With a bit of maturity, I realized that analysis wasn't far off from geometry: Hilbert and Grothendieck made that abundantly clear.

Once you study how shapes move, you've entered dynamics. And the most interesting fact I've discovered thus far is that prime numbers have a shape too.