Patrick Daniels

I work in arithmetic algebraic geometry. These days, I mostly study Shimura varieties using methods from $p$-adic geometry.

Publications and preprints:

Igusa stacks and the cohomology of Shimura varieties, with Pol van Hoften, Dongryul Kim , and Mingjia Zhang, submitted
On a conjecture of Pappas and Rapoport, with Pol van Hoften, Dongryul Kim, and Mingjia Zhang, submitted
Canonical integral models for Shimura varieties of abelian type, with Alex Youcis, Forum of Mathematics, Sigma (2025)
Canonical integral models for Shimura varieties of toral type, Algebra & Number Theory (2025)
$G$-displays of Hodge type and formal $p$-divisible groups , manuscripta mathematica (2024)
A Tannakian framework for $G$-displays and Rapoport–Zink spaces, IMRN (2021)

I also like to work on research projects with undergraduates. I have a few projects in mind which would be accessible to a student who has taken linear algebra and abstract algebra. Feel free to reach out if you are a Skidmore student who is interested in working with me.

Some past projects with undergraduates:

Ekedahl-Oort types of Artin-Schreier curves, Nianchen Liu, University of Michigan REU, 2023
Encoding cohomology, classifying extensions, and explicit Galois gerbes, (co-advised with Alexander Bertoloni Meli and Peter Dillery), Nir Elber and Maxwell Ye, University of Michigan REU, 2022