Tyrone Crisp

Assistant Professor of Mathematics

University of Maine

tyrone.crisp@maine.edu

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.

Teaching

All of my teaching materials are on Brightspace

Research interests

Group representations and operator algebras

Papers

(arXiv versions may differ from published versions)

Frobenius C*-algebras and local adjunctions of C*-correspondences
To appear in International Journal of Mathematics (2021)
[ arXiv ]

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.
[ arXiv ]  [ journal ]

Combinatorial Hopf algebras from representations of families of wreath products
To appear in Algebraic Combinatorics (2021)
Joint with Caleb Kennedy Hill
[ arXiv ]

An inductive approach to representations of general linear groups over compact discrete valuation rings
Preprint (2020)
Joint with Ehud Meir and Uri Onn
[ arXiv ]

Commutativity of the Haagerup tensor product and base change for operator modules
Preprint (2019)
[ arXiv ]

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 ]

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 ]

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 ]

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

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 ]