Photo taken at the Teotihuacán archeological site
I am entering to be a first-year graduate student in mathematics at the University of Pennsylvania in the Fall of 2024. This summer I will be supported as a research fellow at MIT as part of SGI. I completed my undergraduate studies at the University of Southern California (USC) in the Spring of 2024. Broadly speaking, I’m interested in the subject of $\mathbf Q$-points and the interplay between different areas of mathematics with the subject. My research interests fit under the umbrella term of arithmetic geometry. The interplay that I’ve indulged most of my time on is $\mathbf Q$-points and algebraic geometry, but I’m learning more, and becoming more interested, by the Galois theory aspect relating to $\pi_1^{\text{ét}}$.
On this website I will host some notes and slides of mine, a list of more serious papers, and a page for teaching.
I’m currently reading Deligne’s seminal paper, Le Groupe Fondamental de la Droite Projective Moins Trois Points, papers of Minhyong Kim, trying to understand Grothendieck’s program (Esquisse d'un Programme) and finally learning the language of stacks. This past year I did a research project, as part of a course at USC, on Fontaine’s period rings and the de Rham comparison theorem, $\text{H} _{\text{ét}}^n (X _{\overline K}, \mathbf Q _p) \otimes _{\mathbf Q _p} B _\text{dR} \cong \text{H}^n_{\text{dR}} (X) \otimes_K B_{\text{dR}} $ where $X$ is a proper smooth variety over $\text{Spec } K$
I will be fully supported by Penn’s graduate fellowship this upcoming year.
Email: serratos [AT] upenn [DOT] edu
