Napoleon Wang

Department of Math Room 619, University of Arizona, Tucson, AZ

E-mail: napoleonw528[at]arizona.edu

I am a fourth-year math PhD student at the University of Arizona working with Prof. Serin Hong. Here is my CV .

My research interests include Galois deformations, local systems, Hodge structures, and the geometrization of various Hodge theories.

I am based in Seattle for Fall 2026, with potential visits to the Bay Area, the East Coast, and the Midwest. Please feel free to reach out!

Graduate Research: (please see my CV for undergrad research)

Vector bundle extensions on relative Fargues-Fontaine curves: rationality and Galois descent (Extensions of vector bundles on the relative Fargues-Fontaine curve draft; updated preprint will be up around end of Aug 2026)

The first half of the current draft will be split off into detailed introductory notes on perfectoid spaces, adic spaces, and diamonds. It is partially intended to complement the famous Scholze-Weinstein lecture notes by spelling out some underlying details and offering a few more classical analogies and explicit computations.
The upcoming preprint generalizes the vector bundle extension theorem of Birkbeck et al. to the relative setting. It realizes Harder-Narasimhan polygons via extensions, first over a non-algebraically closed perfectoid field, and then over a general perfectoid base via v-covers. It also constructs an explicit counterexample to show how such extensions generally fail to descend to the base, and develops the machinery behind this counterexample into Galois descent criteria.

Explicit Serre-Tate local coordinates of hyperspecial level Shimura varieties (preprint in progress, expected before November)

Motivated by a request from Serin Hong and Alex Youcis to make their existential proofs computable, we develop explicit coordinate descriptions for Serre-Tate deformations of hyperspecial level Shimura varieties upto abelian type (and potentially exceptional types). This work grounds the Serre-Tate theories of Hong, Shankar-Zhou, Imai-Kato-Youcis, and Madapusi-Youcis into entrywise formulas.
We are exploring applications of our display gauge normal form to generalize the foliation of central leaves to exceptional types (prompted by a question from Ananth Shankar), and to compute closed forms of stabilizer actions in the deformation of formal groups.

Online Number Theory Learning Seminars

This series began as a casual reading group in Summer 2025 and continued for three terms. I have had to stop running it for now due to a busy schedule.
However, I am thinking about organizing a joint seminar for students (and maybe postdocs) from different institutes to talk about their (partial) results or what they are currently thinking about, as a way for young people to know what people at other places are working on.

UA Grad ANT Seminar, UA Grad Colloquium

I maintain the seminar websites and help coordinate guest lectures.