You can reach me by email at:
pdaniels (at) skidmore (dot) edu
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, II
with Pol van Hoften, Dongryul Kim, and Mingjia Zhang
preprint (arxiv) - Igusa stacks and the cohomology of Shimura varieties
with Pol van Hoften, Dongryul Kim, and Mingjia Zhang
submitted (arxiv) - On a conjecture of Pappas and Rapoport,
with Pol van Hoften, Dongryul Kim, and Mingjia Zhang
Mathematische Annalen (2026) - 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