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This is my website! I am a Canadian mathematician and an Assistant Professor at Vanderbilt University. I was a Postdoctoral Research Associate at the University of Oxford under the supervision of Stuart White and Dawid Kielak. I earned my PhD in Mathematics at UC San Diego, advised by Adrian Ioana.
My research interests are in operator algebras and interactions with analytic and geometric group theory. You can contact me at gregory.d.patchell[at]vanderbilt.edu. (I will soon lose access to my previous email address, greg.patchell@maths.ox.ac.uk.)
Publications
Lifting for N-independent sets in II1 factors (with A. Shiner). Preprint. September 2026.
Selfless C*-correspondences, operator valued C*-probability spaces and completely positive maps (with D. Gao, M. Junge, S. Kunnawalkam Elayavalli, and L. Robert). Preprint. July 2026.
Selfless reduced amalgamated free products and HNN extensions (with D. Gao, S. Kunnawalkam Elayavalli, and L. Teryoshin). Preprint. April 2026.
A new source of purely finite matricial fields (with D. Gao, S. Kunnawalkam Elayavalli, and A. Manzoor). Preprint. March 2026.
Exotic full factors via weakly coarse bimodules (with D. Gao, D. Jekel, and S. Kunnawalkam Elayavalli). Preprint. January 2026.
Selfless inclusions of C*-algebras (with B. Hayes, S. Kunnawalkam Elayavalli, and L. Robert). Preprint. October 2025.
Some remarks on decay in countable groups and amalgamated free products (with S. Kunnawalkam Elayavalli and L. Teryoshin). Preprint. September 2025.
3-handle construction on II1 factors (with D. Gao and S. Kunnawalkam Elayavalli). Proc. Amer. Math. Soc., accepted (2025).
Strict comparison in reduced group C*-algebras (with T. Amrutam, D. Gao, and S. Kunnawalkam Elayavalli). Invent. Math., (2025). (arXiv)
Simplices of maximally amenable extensions in II1 factors (with S. Kunnawalkam Elayavalli). Groups Geom. Dyn., (2025), published online first. (arXiv)
Sofic actions on graphs (with D. Gao and S. Kunnawalkam Elayavalli). Res. Math. Sci., accepted (2026).
Internal sequential commutation and single generation (with D. Gao, S. Kunnawalkam Elayavalli, and H. Tan). Int. Math. Res. Not., 2025, 8 (2025), rnaf103. (arXiv)
Soficity for group actions on sets and applications (with D. Gao and S. Kunnawalkam Elayavalli). Res. Math. Sci., 12, 3 (2025), Paper No. 48. (arXiv)
On conjugacy and perturbation of subalgebras (with D. Gao, S. Kunnawalkam Elayavalli, and H. Tan). J. Noncommut. Geom., (2025), published online first. (arXiv)
Primeness of generalized wreath product II1 factors. Math. Z., 309, 43 (2025). (arXiv)
Sequential commutation in tracial von Neumann algebras (with S. Kunnawalkam Elayavalli). J. Funct. Anal., 288, 4 (2025), 110719. (arXiv)
The maximum number of appearances of a word in a grid (with S. Spiro). Amer. Math. Monthly, 129, 5 (2022), 415-434. (arXiv)
Computing a multi-location aircraft fleet mix (with S. Wesolkowski and A. Dwarkan). In ICORES (2018), 124-131.
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