Juan Serratos

I'm a researcher in mathematics at the University of Pennsylvania currently working on algebraic geometry and number theory. My recent work focuses on studying the structure of p-adic integer polynomial rings, particularly their prime spectra. I'm interested in creating visual representations of abstract algebraic concepts, following in the tradition of mathematicians like David Mumford. My research combines techniques from algebraic geometry and p-adic analysis to better understand the structural properties of certain polynomial rings. I recently published work examining Spec Zp[T] and creating visual depictions of its structure, drawing parallels with the classical case of Spec Z[T]. This work helps bridge the gap between abstract mathematical concepts and their geometric interpretations.

Prior to my current position, I worked on various mathematical projects, with a particular emphasis on developing new ways to visualize and understand complex mathematical structures. I believe strongly in making advanced mathematical concepts more accessible through geometric and visual representations while maintaining mathematical rigor.