Arnaud Brothier

Senior Lecturer

Since July 2020 (after being a Lecturer for two years) I am a Senior Lecturer (tenure position) in the Department of Pure Mathematics at the University of New South Wales (UNSW) in Sydney. I was previously a Research Assistant at the University of Rome Tor Vergata in the team of Prof Roberto Longo, an Assistant Professor at Vanderbilt University (USA) under the guidance of Prof Dietmar Bisch and a Postdoctoral Researcher in the group of Prof Stefaan Vaes in KU Leuven (Belgium). I was co-supervised by Fields Medallist Vaughan Jones at UC Berkeley and by Prof 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.

 

Journal articles
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Aiello V; Brothier A; Conti R, 2021, 'Jones representations of Thompson’s group F arising from temperley–lieb–jones algebras', International Mathematics Research Notices, vol. 2021, pp. 11209 - 11245, http://dx.doi.org/10.1093/imrn/rnz240
2021
Brothier A; Stottmeister A, 2020, 'Operator-Algebraic Construction of Gauge Theories and Jones’ Actions of Thompson’s Groups', Communications in Mathematical Physics, vol. 376, pp. 841 - 891, http://dx.doi.org/10.1007/s00220-019-03603-4
2020
Brothier A; Jones VFR, 2019, 'Pythagorean representations of Thompson's groups', Journal of Functional Analysis, vol. 277, pp. 2442 - 2469, http://dx.doi.org/10.1016/j.jfa.2019.02.009
2019
Brothier A; Jones VFR, 2019, 'On the Haagerup and Kazhdan properties of R. Thompson's groups', Journal of Group Theory, vol. 22, http://dx.doi.org/10.1515/jgth-2018-0114
2019
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, vol. 361, pp. 81 - 125, http://dx.doi.org/10.1007/s00220-018-3091-2
2018
Boutonnet R; Brothier A, 2018, 'Crossed-products by locally compact groups: Intermediate subfactors', Journal of Operator Theory, vol. 79, pp. 101 - 137, http://dx.doi.org/10.7900/jot.2017jan19.2147
2018
Brothier A; Wen C, 2016, 'The cup subalgebra has the absorbing amenability property', International Journal of Mathematics, vol. 27, http://dx.doi.org/10.1142/S0129167X16500130
2016
Brothier A, 2016, 'On fixed point planar algebras', Journal of Mathematical Physics, vol. 57, http://dx.doi.org/10.1063/1.4967255
2016
Brothier A, 2015, 'Weak amenability for subfactors', International Journal of Mathematics, vol. 26, http://dx.doi.org/10.1142/S0129167X15500482
2015
Brothier A; Vaes S, 2015, 'Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group', Journal of Noncommutative Geometry, vol. 9, pp. 775 - 796, http://dx.doi.org/10.4171/JNCG/207
2015
Brothier A; Jones VFR, 2015, 'Hilbert modules over a planar algebra and the Haagerup property', Journal of Functional Analysis, vol. 269, pp. 3634 - 3644, http://dx.doi.org/10.1016/j.jfa.2015.09.013
2015
Brothier A, 2014, 'The cup subalgebra of a II1 factor given by a subfactor planar algebra is maximal amenable', Pacific Journal of Mathematics, vol. 269, pp. 19 - 29, http://dx.doi.org/10.2140/pjm.2014.269.19
2014
Brothier A; Hartglass M; Penneys D, 2012, 'Rigid C*-tensor categories of bimodules over interpolated free group factors', Journal of Mathematical Physics, vol. 53, http://dx.doi.org/10.1063/1.4769178
2012
Brothier A, 2012, 'Unshaded planar algebras and their associated II 1 factors', Journal of Functional Analysis, vol. 262, pp. 3839 - 3871, http://dx.doi.org/10.1016/j.jfa.2012.02.002
2012
2012
Brothier A, 'Classification of Thompson related groups arising from Jones technology I', , http://arxiv.org/abs/2010.03765v2
Brothier A, 'Classification of Thompson related groups arising from Jones technology II', , http://arxiv.org/abs/2011.13124v1
Brothier A, 'Haagerup property for wreath products constructed with Thompson's groups', , http://arxiv.org/abs/1906.03789v2
Working Papers
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Brothier A; Stottmeister A, Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, http://dx.doi.org, http://arxiv.org/abs/1907.05549v1
Brothier A, On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots, http://dx.doi.org, http://arxiv.org/abs/1912.07140v2

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.

  • 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.
  • Sept.--Dec. 2020. Lecturer for the class Higher Complex Analysis.
  • June--Aug. 2020. Lecturer for the class Functional Analysis.
  • Sept.--Dec. 2019. Lecturer for the class Higher Complex Analysis.
  • Feb.--May 2019. Lecturer for the class Calculus.
  • Aug.--Dec. 2018. Lecturer for the class Complex Analysis.