Tyrone Crisp
Tyrone Crisp
Associate Professor of Mathematics, University of Maine
324 Neville Hall
I came to UMaine in 2018 after positions at Radboud University Nijmegen, the Max Planck Institute for Mathematics in Bonn, and the University of Copenhagen. Before that I studied at Penn State and at the University of Newcastle, Australia.
Research interests
Operator algebras and group representations
Papers
(arXiv versions may differ from published versions)
Trace-class operators on Hilbert modules and Haagerup tensor products
To appear in Journal of Operator Theory (2025)
Joint with Michael Rosbotham
[ arXiv ]
An inductive approach to representations of general linear groups over compact discrete valuation rings
Advances in Mathematics, 440 (2024), Paper no. 109516.
Joint with Ehud Meir and Uri Onn
[ arXiv ] [ journal ]
Functor morphing and representations of automorphism groups of modules
Preprint (2023)
Joint with Ehud Meir and Uri Onn
[ arXiv ]
Flow equivalence of diagram categories and Leavitt path algebras
Journal of Pure and Applied Algebra, 227 (2023), no. 3, 10723.
Joint with Davis MacDonald
[ arXiv ] [ journal ]
If Rm is isomorphic to Rn, must m=n?
The American Mathematical Monthly, 130 (2023), no. 6, 515–521.
[ arXiv ] [ journal ]
Commutativity of the Haagerup tensor product and base change for operator modules
Journal of Topology and Analysis, 15 (2023), no. 4, 1117–1127.
[ arXiv ] [ journal ]
Combinatorial Hopf algebras from representations of families of wreath products
Algebraic Combinatorics, 5 (2022) no. 1, 93-120.
Joint with Caleb Kennedy Hill
[ arXiv ] [ journal ]
Frobenius C*-algebras and local adjunctions of C*-correspondences
International Journal of Mathematics 32 (2021), no. 14, 2150102.
[ arXiv ] [ journal ]
Principal series for general linear groups over finite commutative rings
Communications in Algebra, 49 (2021), no.11, 4857-4868.
Joint with Ehud Meir and Uri Onn
[ arXiv ] [ journal ]
Gluing Hilbert C*-modules over the primitive ideal space
Journal of Functional Analysis 280 (2021), no. 8, 108925.
[ arXiv ] [ journal ]
Descent of Hilbert C*-modules
Journal of Noncommutative Geometry 14 (2020), no. 2, 487–529.
[ arXiv ] [ journal ]
A variant of Harish-Chandra functors
Journal of the Institute of Mathematics of Jussieu 18 (2019), no. 5, 993–1049.
Joint with Ehud Meir and Uri Onn
[ arXiv ] [ journal ]
Frobenius reciprocity and the Haagerup tensor product
Transactions of the American Mathematical Society 370 (2018), no. 10, 6955–6972.
[ arXiv ] [ journal ]
Adjoint functors between categories of Hilbert C*-modules
Journal of the Institute of Mathematics of Jussieu 17 (2018), no. 2, 453–488
Joint with Pierre Clare and Nigel Higson
[ arXiv ] [ journal ]
A second adjoint theorem for SL(2,R)
In “Around Langlands Correspondences”, volume 691 of Contemporary Mathematics, 73–101 (2017)
Joint with Nigel Higson
[ arXiv ] [ journal ]
Parabolic induction and restriction via C*-algebras and Hilbert C*-modules
Compositio Mathematica 152 (2016), 1286–1318
Joint with Pierre Clare and Nigel Higson
[ arXiv ] [ journal ]
Parabolic induction, categories of representations and operator spaces
In “Operator algebras and their applications: a tribute to Richard V. Kadison”, volume 671 of Contemporary Mathematics (2016), 85–109
Joint with Nigel Higson
[ arXiv ] [ journal ]
Parahoric induction and chamber homology for SL2
Journal of Lie Theory 25 (2015), 657–676
[ arXiv ] [ journal ]
Fredholm modules over graph C*-algebras
Bulletin of the Australian Mathematical Society 92 (2015), no. 2, 302–315.
[ arXiv ] [ journal ]
Restriction to compact subgroups in the cyclic homology of reductive p-adic groups
Journal of Functional Analysis 267 (2014), 477–502
[ arXiv ] [ journal ]
The Bost-Connes phase transition and unitary representations
Journal of Noncommutative Geometry 7 (2013), 291–300
[ journal ]
Corners of graph algebras
Journal of Operator Theory 60 (2008), 253–271
[ journal ]
Contractible subgraphs and Morita equivalence of graph C*-algebras
Proceedings of the American Mathematical Society 134 (2006), 2003–2013
Joint with Daniel Gow
[ journal ]
Talks
Frobenius C*-algebras and local adjunctions of C*-correspondences
Video and slides from my talk in the NYC-NCG seminar, September 29, 2021.
[ video ] [ slides ]
C*-algebras of real reductive groups
Video and slides from my lectures at the AIM research community on representation theory and noncommutative geometry, June 2021.
[ lecture 1 ] [ lecture 2 ] [ slides ]
Parabolic induction over the p-adic integers
Video of my talk at the conference on representations of p-adic groups at IISER Pune, July 2017.
[ youtube ]