Researcher

Dr Arnaud Brothier

Keywords

Fields of Research (FoR)

Group Theory and Generalisations, Operator Algebras and Functional Analysis, Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory, Category Theory, K Theory, Homological Algebra

Biography

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...view more

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.

 


My Grants

  • 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.

My Awards

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 Research Activities

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.


My Research Supervision


Areas of supervision

Operator algebras, mathematical physics, group theory, Jones subfactor theory, quantum field theory, von Neumann algebras and more.

I am right now working on a recent connection due to Vaughan Jones between conformal field theory, R. Thompson's groups and knot theory. I would be particularly interested to supervise students in that direction.

I have been recently studying finiteness properties of groups. This involves constructing and studying simplicial complexes and getting informations on their homotopy and homology groups. I would really like to supervise students on this topic.


Currently supervising

  • Dec. 2021-Feb. 2022. Supervisor of Daniel Dunmore for a research project entitled "C*-algebras of discrete groups" sponsored by a AMSI Vacation Research Scholarship and conducted at UNSW Sydney.

  • Feb. 2021--Present. Primary supervisorof Christian de Nicola Larsen for his Ph.D. thesis entitled "Mathematical modelling of field theories" at UNSW Sydney.  The secondary supervisors are Ian Doust and Pinhas Grossman.

  • Feb. 2021--Present. Supervisor of Dilshan Wijesena for his Honours thesis entitled "Irreducible Jones' representations of R. Thompson's groups" at UNSW Sydney.

  • Feb. 2019--Present.  Secondary supervisor of Allan Stoneham for his Ph.D. thesis entitled "Integration theory for AC(sigma) operators" at UNSW Sydney. The primary supervisor is Ian Doust.

My Engagement

  • 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.

My Teaching

  • Sept.--Dec. 2021. Lecturer for the class Higher Complex Analysis.

  • June--Aug. 2021. Lecturer for the class Functional Analysis.

  • 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.

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Location

Red Center Building (H-13), office 6107

Contact

+61-2-9385-7077