John Revere McHugh

Visiting Assistant Professor

I am a Visiting Assistant Professor at the University of Denver in Denver, Colorado, working with Mandi Schaeffer Fry. Prior to moving to Denver, I earned a Ph.D. at the University of California - Santa Cruz under the supervision of Robert Boltje. I also earned a Master's degree at the University of Vermont, under the supervision of Richard Foote.

My research typically deals with representations of finite groups. I am very interested in equivalences between block algebras, fusion systems, biset functors, and (lately) the block theory of finite groups of Lie type.

Publications and Preprints:

J. R. McHugh and A. A. Schaeffer Fry, Real 2-blocks in quasi-simple groups. Awaiting decision. Posted to arXiv May 21, 2026. arXiv identifier: 2605.22969
R. Boltje and J. R. McHugh, Fixed points of extended tensor products. Journal of Algebra 709 (2027), 1-32. DOI: 10.1016/j.jalgebra.2026.05.039
J. R. McHugh, Isotypic blocks of finite groups algebras that are not p-permutation equivalent. Proc. Amer. Math. Soc. 154 (2026) 3681-3692. DOI: 10.1090/proc/17701
J. R. McHugh, Coherence conditions for the characters of trivial source modules and strong isotypies. Posted to arXiv October 16, 2023. arXiv identifier: 2310.10880
J. R. McHugh, On the image of the trivial source ring in the ring of virtual characters of a finite group. Pacific Journal of Mathematics 315 (2021), no. 2, 449-476. DOI: 10.2140/pjm.2021.315.449

In Preparation:

R. Boltje, J. R. McHugh, N. Monteiro, Links between character triples.
J. Lynd, J. R. McHugh, A. A. Schaeffer Fry, On the Külshammer-Puig classes of unipotent blocks.
A. Farmar, J. R. McHugh, Schur indices and Brauer's 14th problem: an approach via biset functors.

Theses:

Strong Isotypies and Coherent Character Tuples. Ph.D. Thesis, University of California, Santa Cruz, 2024. Advisor: Robert Boltje.
Monomial Characters of Finite Groups. M.S. Thesis, University of Vermont, 2016. Advisor: Richard Foote.

Recent Activity:

Together with Radha Kessar, Nariel Monteiro, and Deniz Yılmaz, I co-organized the conference Representations of Finite Groups and Related Structures. This conference was held at the University of California - Santa Cruz in August 2026, and brought together experts and young researchers from all over the world to discuss the latest advancements in representation theory.
I am the organizer of the math department's Algebra & Logic Seminar at the University of Denver. See this webpage for a list of upcoming and past talks!
In March of 2026, I visited Justin Lynd at the University of Louisiana at Lafayette, and spoke in the Algebra Seminar there.
I attended and spoke in the special session on Groups and Representation Theory at the Fall 2025 AMS Sectional Meeting in St. Louis, MO.
In May of 2025 I attended and spoke at the AWM Research Symposium in Madison, WI.
In January of 2025 I attended the conference Characters and Blocks of Finite Groups: Celebrating Gabriel Navarro's 60th Birthday in beautiful Valencia, Spain.

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