Articles

Publications

(21) (Joint with Dilshan Wijesena). Jones' representations of R. Thompson's groups not induced by finite dimensional ones, to appear in Annales de l'institut Fourier (ISSN: 0373-0956), available at arXiv:2211.08555.
(20) Forest-skein groups II: construction from homogeneously presented monoids, International Journal of Mathematics (ISSN: 0129-167X), Vol. 34, Issue 8, 2350042, 2023, available at arXiv:2212.01993, journal article. N.B. There is an imprecision in the journal article. An updated corrected version is uploaded on the arxiv server.
(19) Haagerup property for wreath products constructed with Thompson's groups, Groups, Geometry, and Dynamics (ISSN: 1661-7215), Vol. 17, Issue 2, pp. 671--718, 2023, available at arXiv:1906.03789, article.
(18) Classification of Thompson related groups arising from Jones technology I, International Mathematics Research Notice (ISSN: 1073-7928), Vol. 2023, Issue 7, pp. 5974--6044, article, available at arXiv:2010.03765.
(17) Classification of Thompson related groups arising from Jones technology II, Bulletin de la Société Mathématiques de France (ISSN: 0037-9484), Vol. 149, Issue 4 (2021) pp. 663-725, article, available at arXiv:2011.13124.
(16) On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots, Celebratio Mathematica, in the volume on Vaughan F. R. Jones, available at arXiv:1912.07140, article.
(15) (Joint with Alexander Stottmeister). Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups, Communication in Mathematical Physics (ISSN: 0010-3616), Vol. 376 (2020) pp. 841–891, available at arXiv:1901.04940, https://doi.org/10.1007/s00220-019-03603-4, view-only link.
(14) (Joint with Valeriano Aiello and Roberto Conti), Jones representations of Thompson’s group F arising from Temperley-Lieb-Jones algebras, International Mathematics Research Notices (ISSN: 1073-7928), Vol. 15 (2021) pp. 11209-11245, available at arXiv:1901.10597, article, https://doi.org/10.1093/imrn/rnz240.
(13) (Joint with Vaughan Jones). On the Haagerup and Kazhdan properties of R. Thompson's groups, Journal of Group Theory (ISSN: 1433-5883), Vol. 22, Issue 5 (2019) pp. 795-807, available at arXiv:1805.02177, article, https://doi.org/10.1515/jgth-2018-0114.
(12) (Joint with Vaughan Jones). Pythagorean representations of Thompson's groups, Journal of Functional Analysis (ISSN: 0022-1236), Vol. 277 (2019) 2442-2469, available at arXiv:1807.06215, article, https://doi.org/10.1016/j.jfa.2019.02.009.
(11) (Joint with Tobe Deprez and Stefaan Vaes). Rigidity for von Neumann algebras given by locally compact groups and their crossed products, Communications in Mathematical Physics (ISSN: 0010-3616), Vol. 361, Issue 1 (2018) pp. 81-125, available at arXiv:1703.09092, article, https://doi.org/10.1007/s00220-018-3091-2.
(10) (Joint with Rémi Boutonnet). Crossed-products by locally compact groups: Intermediate subfactors, Journal of Operator Theory (ISSN: 0379-4024), Vol. 79, Issue 1 (2018) pp. 101-137, available at arXiv:1611.10121, article, DOI: 10.7900/jot.2017jan19.2147.
(9) On fixed point planar algebras, Journal of Mathematical Physics (ISSN: 0022-2488), Vol. 57 (2016) pp. 111703 available at arXiv:1603.01205, article, https://doi.org/10.1063/1.4967255.
(8) (Joint with Chenxu Wen). The cup subalgebra has the absorbing amenability property, International Journal of Mathematics (ISSN: 0129-167X), Vol. 27, No. 2 (2016) pp. 1650013, available at arXiv:1510.06075,article, https://doi.org/10.1142/S0129167X16500130.
(7) (Joint with Vaughan Jones). Hilbert modules over a planar algebra and the Haagerup property, Journal of Functional Analysis, Vol. 269 (2015) pp. 3634-3644, available at arXiv:1503.02708, article, http://dx.doi.org/10.1016/j.jfa.2015.09.013.
(6) Weak amenability for subfactors, International Journal of Mathematics (ISSN: 0129-167X), Vol. 26, No. 5 (2015) pp. 1550048, available at arXiv:1410.2875, article, http://dx.doi.org/10.1142/S0129167X15500482.
(5) (Joint with Stefaan Vaes). Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group, Journal of Noncommutative Geometry (ISSN: 1661-6952), Vol. 9 (2015) pp. 775-796, available atarXiv:1309.5354, article, http://dx.doi.org/10.4171/JNCG/207.
(4) The cup subalgebra of a II_1 factor given by a subfactor planar algebra is maximal amenable, Pacific Journal of Mathematics (ISSN: 0030-8730), Vol. 269, No. 1 (2014) pp. 19-29, available at arXiv:1210.8091,article, http://dx.doi.org/10.2140/pjm.2014.269.19.
(3) (Joint with Michael Hartglass and David Penneys). Rigid C*-tensor categories of bimodules over interpolated free group factors, Journal of Mathematical Physics (ISSN: 0022-2488), Vol. 53 (2012) pp. 123525, available at arXiv:1208.5505, article, http://dx.doi.org/10.1063/1.4769178.
(2) The Takesaki equivalence relation for maximal abelian subalgebras, Munster Journal of Mathematics (ISSN: 1867-5778), Vol. 5 (2012) pp. 59-72, available at arXiv:1111.6846, article.
(1) Unshaded planar algebras and their associated II_1 factors, Journal of Functional Analysis (ISSN: 0022-1236), Vol. 262, Issue 9 (2012) pp. 3839-3871, available at arXiv:1202.1298,article, http://dx.doi.org/10.1016/j.jfa.2012.02.002.

Preprints

(6) (Joint with Ryan Seelig). Forest-skein groups III: simplicity, Preprint 2024, available at arXiv:2406.09718.
(5) (Joint with Dilshan Wijesena). Atomic representations of R. Thompson's group and Cuntz's algebra, Preprint 2024, available at arXiv:2406.02967.
(4) (Joint with Dilshan Wijesena). Irreducible representations of R. Thompson's groups and of the Cuntz algebra, Preprint 2023, available at arXiv:2306.01256.
(3) (Joint with Dilshan Wijesena). Decomposition of Pythagorean representations of R. Thompson's groups, Preprint 2023, available at arXiv:2302.04458.
(2) Forest-skein groups I: between Jones' subfactors and R. Thompson's groups, Preprint 2022, available at arXiv:2207.03100.
(1) (Joint with Alexander Stottmeister). Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, Preprint 2019, available at arXiv:1907.05549.