Eamon Quinlan-Gallego

Email: (my first name)qg AT uic DOT edu
Office: JWB 209

I am a Research Assistant Professor (postdoc) in the Department of Mathematics, Statistics, and Computer Science of the University of Illinois at Chicago. Before that I was an NSF-funded postdoc in the Department of Mathematics of the University of Utah, and prior to that a graduate student at University of Michigan, where my advisor was Karen Smith. I got my undergraduate degree from the University of Glasgow, and I am from El Escorial, in Spain.

You can see my CV here, last updated on August 2025.

 

Research: I am interested in rings of differential operators and their applications to commutative algebra and algebraic geometry. In particular, I have been studying positive-characteristic analogues of Bernstein-Sato polynomials and the structure of rings of differential operators on singular algebras.

• Plus-pure thresholds of some cusp-like singularities in mixed characteristic. arXiv.
  With H. Cai, S. Pande, K. Schwede and K. Tucker
  
• Bernstein-Sato theory modulo p^m. arXiv.
  With T. Bitoun.
  Submitted
• Flat morphisms with regular fibers do not preserve F-rationality. arXiv.
  With A. Simpson and A. Singh.
  Revista Matemática Iberoamericana, 2024.
• A formalism of F-modules for rings with complete local finite F-representation type. arXiv.
  International Mathematics Research Notices, 2024.
• Bernstein-Sato theory for singular rings in positive characteristic. arXiv.
  With J. Jeffries and L. Núñez-Betancourt.
  Transactions of the AMS, 2023.
• Symmetry on rings of differential operators. arXiv.
  Journal of Algebra, 2021.
• Bernstein-Sato roots for monomial ideals in positive characteristic. arXiv.
  Nagoya Math Journal, 2020.
• Bernstein-Sato theory for arbitrary ideals in positive characteristic. arXiv.
  Transactions of the AMS, 2020.

Notes: All comments welcome and appreciated!

• My thesis: Bernstein-Sato theory in positive characteristic. PDF.
• A Lecture Series on Differential Operators. PDF.
• Morita equivalence. PDF.
• Analysis notes for the QR exam at the University of Michigan. PDF.
• Slides for my talk at the 41st Japan Symposium on Commutative Algebra. PDF.

Teaching:

• Fall 2023: MATH1220 Calculus II.
• Summer 2022: Summer High School Program.
• Spring 2022: MATH3160 Applied Complex Variables.
• Fall 2021: MATH1220 Calculus II.
• Fall 2020: MATH116 Calculus II (Graduate Student Instructor).
• Winter 2020: MATH116 Calculus II (Graduate Student Instructor).
• Summer 2018: Fibonacci Numbers [MMSS] (Course Assistant).
• Summer 2017: Fibonacci Numbers [MMSS] (Course Assistant).
• Winter 2017: MATH115 Calculus I (Graduate Student Instructor).
• Fall 2016: MATH105 Precalculus (Graduate Student Instructor).

Thesis template: Angus Chung and I developed a thesis template for LaTeX which is compatible with the requirements of the Rackham Graduate School, to which Yifeng Huang made later improvements. You can find the most up-to-date version of the template (as of April 2022) here. The template has a few shortcomings, which are detailed in the README file. If you find a way to overcome them or otherwise improve the template, please let me know!

The opinions, findings, conclusions or recommendations expressed here are mine and do not necessarily reflect the views of the National Science Foundation.