Xinyu Zhou's Homepage

Me and a very tall cactus at AWS 2025.

Hi, my name is Xinyu Zhou. I am a PhD student at Boston University. My main interest is arithmetic geometry. Recently, I am more focusing on some problems in p-adic geometry and the geometry of moduli spaces of shtukas. Currently, I am working on applications of p-adic cohomology of diamonds to chromatic homotopy theory

My Email Address is xyz6 (at) bu.edu
My office is CDS 345.

CV: Link

Teaching:

Summer 2025 MA226S A2: Differential Equations

Research:

On the Langlands-Kottwitz Method for Drinfeld Modular Varieties at Bad Primes(In preparation)
We use Scholze's approach on Langlands-Kottwitz method for some Shimura varieties to determine the (semisimple) local factors of the Hasse-Weil zeta functions of Drinfeld modular varieties at bad primes. In this process, we overcome several difficuties that do not appear in the Shimura variety case. We also give a construction of the "canonical level structure" map for Drinfeld modular varieties, which gives reduced fibers at bad primes and also leads to a more general duality theory for Drinfeld modules.

Seminar:

Learning Seminar on Prismatic Cohomology

BUNTES 2024: Automorphic Representations

Notes:

Here are some notes I wrote.
Intersection Theory. These notes give introductions to Chern classes and Segre classes on schemes.
Brauer-Manin Obstructions. This is the note for the STAGE talk at MIT on the étale Brauer obstructions and insufficiencies.
Formal Vanishing Cycles. These are the notes for my talk at a learning seminar on Scholze's proof of Local Langlands for \(GL_n\). I discussed some basic properties of formal vanishing cycles and deformation spaces of divisible modules.
Verdier duality. Introduction to Verdier duality
Ramanujan-Petersson Conjecture--Part 1. An introduction to the Ramanujan-Petersson conjecture.
Introduction to divided power structures. Elementary. It has a detailed example of non-uniqueness of PD structures. So it may be helpful if you are looking for examples.

Useful Links:

World's cutest animals.
Memorial article for Rosa the sea otter on New York Times.
A shtuka with two paws.

Return to Math's home page