Patrick Daniels Department of Mathematics and Statistics · Skidmore College
Portrait of Patrick Daniels

About Me

I'm an Assistant Professor of Mathematics at Skidmore College. My research concerns integral models of Shimura varieties, p-adic shtukas and displays, and the p-adic geometry of Shimura varieties.

Email Google Scholar arXiv

Research

My research is in arithmetic algebraic geometry. I am particularly interested in integral models of Shimura varieties, p-adic shtukas and displays, and Igusa stacks and their applications to the cohomology of Shimura varieties. Recently, together with some Skidmore undergraduates, I have been studying the Ekedahl–Oort types of some Artin–Schreier curves.

Recent work

  1. Igusa stacks and the cohomology of Shimura varieties, II

    with Pol van Hoften, Dongryul Kim, and Mingjia Zhang

    Submitted

    arXiv

  2. Igusa stacks and the cohomology of Shimura varieties

    with Pol van Hoften, Dongryul Kim, and Mingjia Zhang

    Submitted

    arXiv

  3. On a conjecture of Pappas and Rapoport

    with Pol van Hoften, Dongryul Kim, and Mingjia Zhang

    Mathematische Annalen, 2026

    arXivJournal

Other publications

  1. Canonical integral models for Shimura varieties of abelian type

    with Alex Youcis

    Forum of Mathematics, Sigma, 2025

    Journal
  2. Journal
  3. Journal

  4. A Tannakian framework for G-displays and Rapoport–Zink spaces

    International Mathematics Research Notices, 2021

    Journal

Students

Undergraduate research

I enjoy working with undergraduates on projects in algebra, number theory, and arithmetic geometry. I have several projects accessible after linear algebra and abstract algebra. Skidmore students interested in research or a reading course are welcome to contact me.

Teaching

At Skidmore, I teach courses across the mathematics curriculum, from calculus and linear algebra to proof-based courses in analysis, algebra, and number theory. Course information for enrolled students is available through Brightspace.

Selected advanced courses

  • MA 351 Modern Number Theory
  • MA 319 Abstract Algebra I
  • MA 303 Introduction to Analysis
  • MA 215 Intro to Proofs

Foundational courses

  • MA 213 Calculus IV
  • MA 200 Linear Algebra
  • MA 113 Calculus II
  • MA 111 Calculus I

Bio

Before joining Skidmore in 2023, I was a postdoctoral assistant professor at the University of Michigan. I received my PhD from the University of Maryland in 2020 under the supervision of Thomas Haines. Before that, I completed undergraduate degrees in Economics and Mathematics at SUNY Geneseo.