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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 , an Assistant Professor at Vanderbilt University (USA) under the guidance of Professor and a Postdoctoral Researcher in the group of Professor in KU Leuven (Belgium).

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

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

Phone
+61-2-9385-7077
Location
Red Center Building (H-13), office 6107
  • 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,
    Journal articles | 2023
    Brothier A, 2023, 'Classification of Thompson Related Groups Arising from Jones Technology I', International Mathematics Research Notices, 2023, pp. 5974 - 6044,
    Journal articles | 2023
    Brothier A, 2023, 'Forest-skein groups II: Construction from homogeneously presented monoids', International Journal of Mathematics, 34,
    Journal articles | 2023
    Brothier A, 2023, 'Haagerup property for wreath products constructed with Thompson’s groups', Groups, Geometry, and Dynamics, 17, pp. 671 - 718,
    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,
    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,
    Journal articles | 2020
    Brothier A, 2020, 'Classification of Thompson related groups arising from Jones technology I', ,
    Journal articles | 2020
    Brothier A, 2020, 'Classification of Thompson related groups arising from Jones technology II', ,
    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,
    Journal articles | 2019
    Brothier A; Jones VFR, 2019, 'Pythagorean representations of Thompson's groups', Journal of Functional Analysis, 277, pp. 2442 - 2469,
    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,
    Journal articles | 2018
    Boutonnet R; Brothier A, 2018, 'Crossed-products by locally compact groups: Intermediate subfactors', Journal of Operator Theory, 79, pp. 101 - 137,
    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,
    Journal articles | 2016
    Brothier A; Wen C, 2016, 'The cup subalgebra has the absorbing amenability property', International Journal of Mathematics, 27,
    Journal articles | 2016
    Brothier A, 2016, 'On fixed point planar algebras', Journal of Mathematical Physics, 57,
    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,
    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,
    Journal articles | 2015
    Brothier A, 2015, 'Weak amenability for subfactors', International Journal of Mathematics, 26,
    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,
    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,
    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,
  • Working Papers | 2019
    Brothier A; Stottmeister A, 2019, Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, ,
    Working Papers | 2019
    Brothier A, 2019, On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots, ,
  • Preprints | 2024
    Brothier A; Seelig R, 2024, Forest-skein groups III: simplicity, ,
    Preprints | 2024
    Brothier A; Wijesena D, 2024, Atomic representations of R. Thompson's groups and Cuntz's algebra, ,
    Preprints | 2023
    Brothier A; Wijesena D, 2023, Decomposition of Pythagorean representations of R. Thompson's groups, ,
    Preprints | 2023
    Brothier A; Wijesena D, 2023, Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra, ,
    Preprints | 2022
    Brothier A; Wijesena D, 2022, Jones' representations of R. Thompson's groups not induced by finite-dimensional ones, ,
    Preprints | 2022
    Brothier A, 2022, Forest-skein groups I: between Vaughan Jones' subfactors and Richard Thompson's groups, ,
    Preprints | 2022
    Brothier A, 2022, Forest-skein groups II: construction from homogeneously presented monoids, ,
    Preprints | 2019
    Aiello V; Brothier A; Conti R, 2019, Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras, ,
    Preprints | 2019
    Brothier A; Stottmeister A, 2019, Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach, ,
    Preprints | 2019
    Brothier A; Stottmeister A, 2019, Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups, ,

  • 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.
  • February2019 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-August2016. NSF summer support sponsored by Vaughan Jones.
  • June-August2015. NSF summer support sponsored by Vaughan Jones.
  • July-August2010. 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.
  • September2008 -- Aug. 2011. Full grant scholarship, Ph.D. program fellowship of Region Iles de France.
  • September2004 -- Aug. 2008. Full grant scholarship as a student of ENS Cachan.

2016. Winner of the 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 and ). 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 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 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 .
  • 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.