Back to
Dr Arnaud Brothier

Dr Arnaud Brothier

Senior Lecturer
Science
School of Mathematics & Statistics

Since July 2020 I am a Senior Lecturer (tenure position)  in the Department of Pure Mathematics at the University of New South Wales (UNSW) in Sydney that I joined in July 2018 as a Lecturer.

I was previously a Research Assistant at the University of Rome Tor Vergata in the team of Professor Roberto Longo, an Assistant Professor at Vanderbilt University (USA) under the guidance of Professor Dietmar Bisch and a Postdoctoral Researcher in the group of Professor Stefaan Vaes in KU Leuven (Belgium). 

I was honoured to be co-supervised by  Fields Medalist Vaughan Jones at UC Berkeley and by Professor Andrzej Zuk at the University of Paris Diderot for my Ph.D. that I completed in 2011 in Paris.

Here is an interview of myself (in french) realized by Camille Saumard for the company LumenAi.

 
Phone
+61-2-9385-7077
E-mail
a.brothier@unsw.edu.au
Location
Red Center Building (H-13), office 6107
  • Journal articles | 2026
    Brothier A; Seelig R, 2026, 'Finitely presented simple groups with no piecewise projective actions', Journal of the London Mathematical Society, 113, http://dx.doi.org/10.1112/jlms.70436
    Journal articles | 2026
    Brothier A; Wijesena D, 2026, 'Atomic representations of R. Thompson’s groups and Cuntz’s algebra', Documenta Mathematica, 31, pp. 355 - 383, http://dx.doi.org/10.4171/dm/1031
    Journal articles | 2025
    Brothier A; Wijesena D, 2025, 'A Tensor Product for Representations of the Cuntz Algebra and of the R. Thompson Groups', Communications in Mathematical Physics, 406, http://dx.doi.org/10.1007/s00220-025-05331-4
    Journal articles | 2025
    Brothier A; Wijesena D, 2025, 'JONES’ REPRESENTATIONS OF R. THOMPSON’S GROUPS NOT INDUCED BY FINITE-DIMENSIONAL ONES', Annales De L Institut Fourier, 75, pp. 2677 - 2716, http://dx.doi.org/10.5802/aif.3689
    Journal articles | 2024
    Brothier A; Wijesena D, 2024, 'Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra', Advances in Mathematics, 454, http://dx.doi.org/10.1016/j.aim.2024.109871
    Journal articles | 2023
    Brothier A, 2023, 'Classification of Thompson Related Groups Arising from Jones Technology I', International Mathematics Research Notices, 2023, pp. 5974 - 6044, http://dx.doi.org/10.1093/imrn/rnac031
    Journal articles | 2023
    Brothier A, 2023, 'Forest-skein groups II: Construction from homogeneously presented monoids', International Journal of Mathematics, 34, http://dx.doi.org/10.1142/S0129167X23500428
    Journal articles | 2023
    Brothier A, 2023, 'Haagerup property for wreath products constructed with Thompson’s groups', Groups Geometry and Dynamics, 17, pp. 671 - 718, http://dx.doi.org/10.4171/GGD/714
    Journal articles | 2021
    Aiello V; Brothier A; Conti R, 2021, 'Jones representations of Thompson’s group F arising from temperley–lieb–jones algebras', International Mathematics Research Notices, 2021, pp. 11209 - 11245, http://dx.doi.org/10.1093/imrn/rnz240
    Journal articles | 2021
    Brothier A, 2021, 'CLASSIFICATION OF THOMPSON RELATED GROUPS ARISING FROM JONES' TECHNOLOGY II', Bulletin De La Societe Mathematique De France, 149, pp. 663 - 725, http://dx.doi.org/10.24033/bsmf.2841
    Journal articles | 2020
    Brothier A; Stottmeister A, 2020, 'Operator-Algebraic Construction of Gauge Theories and Jones’ Actions of Thompson’s Groups', Communications in Mathematical Physics, 376, pp. 841 - 891, http://dx.doi.org/10.1007/s00220-019-03603-4
    Journal articles | 2020
    Brothier A, 2020, 'Classification of Thompson related groups arising from Jones technology I', , http://arxiv.org/abs/2010.03765v3
    Journal articles | 2020
    Brothier A, 2020, 'Classification of Thompson related groups arising from Jones technology II', , http://arxiv.org/abs/2011.13124v2
    Journal articles | 2019
    Brothier A; Jones VFR, 2019, 'On the Haagerup and Kazhdan properties of R. Thompson's groups', Journal of Group Theory, 22, pp. 795 - 807, http://dx.doi.org/10.1515/jgth-2018-0114
    Journal articles | 2019
    Brothier A; Jones VFR, 2019, 'Pythagorean representations of Thompson's groups', Journal of Functional Analysis, 277, pp. 2442 - 2469, http://dx.doi.org/10.1016/j.jfa.2019.02.009
    Journal articles | 2019
    Brothier A, 2019, 'Haagerup property for wreath products constructed with Thompson's groups', Groups, Geometry, and Dynamics Volume 17, Issue 2, pages 671--718, 2023, http://arxiv.org/abs/1906.03789v3
    Journal articles | 2018
    Boutonnet R; Brothier A, 2018, 'Crossed-products by locally compact groups: Intermediate subfactors', Journal of Operator Theory, 79, pp. 101 - 137, http://dx.doi.org/10.7900/jot.2017jan19.2147
    Journal articles | 2018
    Brothier A; Deprez T; Vaes S, 2018, 'Rigidity for Von Neumann Algebras Given by Locally Compact Groups and Their Crossed Products', Communications in Mathematical Physics, 361, pp. 81 - 125, http://dx.doi.org/10.1007/s00220-018-3091-2
    Journal articles | 2016
    Brothier A; Wen C, 2016, 'The cup subalgebra has the absorbing amenability property', International Journal of Mathematics, 27, http://dx.doi.org/10.1142/S0129167X16500130
    Journal articles | 2016
    Brothier A, 2016, 'On fixed point planar algebras', Journal of Mathematical Physics, 57, http://dx.doi.org/10.1063/1.4967255
    Journal articles | 2015
    Brothier A; Jones VFR, 2015, 'Hilbert modules over a planar algebra and the Haagerup property', Journal of Functional Analysis, 269, pp. 3634 - 3644, http://dx.doi.org/10.1016/j.jfa.2015.09.013
    Journal articles | 2015
    Brothier A; Vaes S, 2015, 'Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group', Journal of Noncommutative Geometry, 9, pp. 775 - 796, http://dx.doi.org/10.4171/JNCG/207
    Journal articles | 2015
    Brothier A, 2015, 'Weak amenability for subfactors', International Journal of Mathematics, 26, http://dx.doi.org/10.1142/S0129167X15500482
    Journal articles | 2014
    Brothier A, 2014, 'The cup subalgebra of a II1 factor given by a subfactor planar algebra is maximal amenable', Pacific Journal of Mathematics, 269, pp. 19 - 29, http://dx.doi.org/10.2140/pjm.2014.269.19
    Journal articles | 2012
    Brothier A; Hartglass M; Penneys D, 2012, 'Rigid C*-tensor categories of bimodules over interpolated free group factors', Journal of Mathematical Physics, 53, http://dx.doi.org/10.1063/1.4769178
    Journal articles | 2012
    Brothier A, 2012, 'The Takesaki equivalence relation for maximal abelian subalgebras', MUENSTER JOURNAL OF MATHEMATICS, 5, pp. 59 - 71
    Journal articles | 2012
    Brothier A, 2012, 'Unshaded planar algebras and their associated II 1 factors', Journal of Functional Analysis, 262, pp. 3839 - 3871, http://dx.doi.org/10.1016/j.jfa.2012.02.002
  • Working Papers | 2019
    Brothier A; Stottmeister A, 2019, Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, http://dx.doi.org, http://arxiv.org/abs/1907.05549v1
    Working Papers | 2019
    Brothier A, 2019, On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots, http://dx.doi.org, http://arxiv.org/abs/1912.07140v2
  • Preprints | 2026
    Brothier A; Sims A; Wijesena D, 2026, Classification of representations of higher-rank graph C*-algebras
    Preprints | 2025
    Brothier A; Seelig R, 2025, Finitely presented simple groups with no piecewise projective actions, http://dx.doi.org/10.48550/arxiv.2512.18943
    Preprints | 2024
    Brothier A; Seelig R, 2024, Forest-skein groups III: simplicity, http://arxiv.org/abs/2406.09718v1
    Preprints | 2024
    Brothier A; Seelig R, 2024, Forest-skein groups IV: dynamics, http://arxiv.org/abs/2411.12569v1
    Preprints | 2024
    Brothier A; Wijesena D, 2024, A tensor product for representations of the Cuntz algebra and of the R. Thompson groups, http://arxiv.org/abs/2408.12051v1
    Preprints | 2024
    Brothier A; Wijesena D, 2024, Atomic representations of R. Thompson's groups and Cuntz's algebra, http://arxiv.org/abs/2406.02967v1
    Preprints | 2024
    Brothier A; Wijesena D, 2024, Moduli of representations of Leavitt path algebras, http://arxiv.org/abs/2412.09163v1
    Preprints | 2023
    Brothier A; Wijesena D, 2023, Decomposition of Pythagorean representations of R. Thompson's groups, http://arxiv.org/abs/2302.04458v2
    Preprints | 2023
    Brothier A; Wijesena D, 2023, Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra, http://dx.doi.org/10.1016/j.aim.2024.109871
    Preprints | 2022
    Brothier A; Wijesena D, 2022, Jones' representations of R. Thompson's groups not induced by finite-dimensional ones, http://arxiv.org/abs/2211.08555v1
    Preprints | 2022
    Brothier A, 2022, Forest-skein groups I: between Vaughan Jones' subfactors and Richard Thompson's groups, , http://arxiv.org/abs/2207.03100v2
    Preprints | 2022
    Brothier A, 2022, Forest-skein groups II: construction from homogeneously presented monoids, , http://arxiv.org/abs/2212.01993v2
    Preprints | 2020
    Brothier A, 2020, Classification of Thompson related groups arising from Jones technology I, http://arxiv.org/abs/2010.03765v3
    Preprints | 2020
    Brothier A, 2020, Classification of Thompson related groups arising from Jones technology II, http://arxiv.org/abs/2011.13124v2
    Preprints | 2019
    Aiello V; Brothier A; Conti R, 2019, Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras, http://dx.doi.org/10.1093/imrn/rnz240
    Preprints | 2019
    Brothier A; Stottmeister A, 2019, Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, http://dx.doi.org/10.48550/arxiv.1907.05549
    Preprints | 2019
    Brothier A; Stottmeister A, 2019, Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups, http://dx.doi.org/10.1007/s00220-019-03603-4
    Preprints | 2018
    Brothier A; Jones VFR, 2018, On the Haagerup and Kazhdan properties of R. Thompson's groups, http://arxiv.org/abs/1805.02177v1
    Preprints | 2018
    Brothier A; Jones VFR, 2018, Pythagorean representations of Thompson's groups, http://arxiv.org/abs/1807.06215v1
    Preprints | 2017
    Brothier A; Deprez T; Vaes S, 2017, Rigidity for von Neumann algebras given by locally compact groups and their crossed products, http://dx.doi.org/10.48550/arxiv.1703.09092
    Preprints | 2016
    Boutonnet R; Brothier A, 2016, Crossed-products by locally compact groups: Intermediate subfactors, http://arxiv.org/abs/1611.10121v2
    Preprints | 2016
    Brothier A, 2016, On fixed point planar algebras, http://dx.doi.org/10.1063/1.4967255
    Preprints | 2015
    Brothier A; Jones V, 2015, Hilbert modules over a planar algebra and the Haagerup property, http://arxiv.org/abs/1503.02708v1
    Preprints | 2015
    Brothier A; Wen C, 2015, The cup subalgebra has the absorbing amenability property, http://arxiv.org/abs/1510.06075v2
    Preprints | 2014
    Brothier A, 2014, Weak amenability for subfactors, http://arxiv.org/abs/1410.2875v2
    Preprints | 2013
    Brothier A; Vaes S, 2013, Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group, http://arxiv.org/abs/1309.5354v1
    Preprints | 2012
    Brothier A; Hartglass M; Penneys D, 2012, Rigid C^*-tensor categories of bimodules over interpolated free group factors, http://dx.doi.org/10.1063/1.4769178
    Preprints | 2012
    Brothier A, 2012, The cup subalgebra of a II_1 factor given by a subfactor planar algebra is maximal amenable, http://dx.doi.org/10.2140/pjm.2014.269.19
    Preprints | 2012
    Brothier A, 2012, Unshaded planar algebras and their associated II_1 factors, http://arxiv.org/abs/1202.1298v1
    Preprints | 2011
    Brothier A, 2011, The Takesaki equivalence relation for maximal abelian subalgebras, http://arxiv.org/abs/1111.6846v1

  • January 2020--December 2022. ARC (Australian Research Council) Discovery Project DP200100067: Physical realisation of enriched quantum symmetries joint with Pinhas Grossman, Scott Morrison and James Tener.
  • February 2019 AMSI Scientific Workshop Funding with additional support of AustMS, “Subfactors in Sydney”.
  • July 2018--June 2020. University of New South Wales Sydney Starting Grant.
  • June 2016. Short stay support sponsored by the Hausdorff Research Institute for Mathematics.
  • June-August 2016. NSF summer support sponsored by Vaughan Jones.
  • June-August 2015. NSF summer support sponsored by Vaughan Jones.
  • July-August 2010. Short stay support sponsored by the Mathematical Foundation of France for the ICM 2010 in Hyderabad in India.
  • March-May 2009. Short stay support sponsored by the Mathematical Foundation of Paris for visiting UC Berkeley.
  • September 2008 -- Aug. 2011. Full grant scholarship, Ph.D. program fellowship of Region Iles de France.
  • September 2004 -- Aug. 2008. Full grant scholarship as a student of ENS Cachan.

2016. Winner of the Samir Aldroubi and Amira Azhari Prize for Excellence in Postdoctoral Research which is awarded every two years to recognize the research achievements of current and recent postdoctoral fellows in the department of Mathematics of Vanderbilt University, USA.

My mathematical education was on operator algebras with a focus on the theory of von Neumann algebras which is a mixed of functional analysis and linear algebras introduced to describe quantum mechanics. It provides powerful tools for ergodic theory, infinite group theory and a large part of theoretical physics.
 
I mainly work in operator algebras and its connections with group theory, ergodic theory, representation theory, and quantum field theory. I am an expert in Jones subfactor theory which connects deeply conformal field theory, low dimensional topology and von Neumann algebras.
 
Since 2016 I have been involved in a new and exciting connection that Jones made between subfactor theory, quantum field theory, knot theory and Richard Thompson group (see Jones survey and mine). I have been particularly interested to applications toward group theory and quantum field theory using subfactor's ideas.
 

Some of my recent themes of interest include the following:

-Operator algebraic treatment of lattice gauge theories;

-Actions of Thompson groups constructed via Jones' technology;

-Actions of locally compact groups on von Neumann algebras;

-Classification and analytical properties of subfactors/tensor categories.

  • April 2020--Present. Contributing editor of the online magazine Parabola published by the School of Mathematics and Statistics of UNSW (first as a Problem Editor until March 2022 and then as Assistant Chief Editor).
  • March 2020--Dec. 2022. Organiser of the Pure Math Seminar at UNSW.
  • March 2020--Dec. 2022. Co-organiser of the Joint Colloquium of Mathematics of University of Sydney and UNSW.
  • January 2020--Present. Member of the Australian and New Zealand Association of Mathematical Physics.
  • July 2018--Feb. 2022. Member of the Publicity committee at UNSW.
  • Reviewer for scientific journals, e.g. Bulletin of the London Mathematical Society, Communication in Mathematical Physics, Journal of Combinatorial Algebra , Proceeding of Mathematical Sciences, Physical Review Letters.