Researcher

Dr Arnaud Brothier

Keywords

Field of Research (FoR)

Biography

Since July 2018 I am a Lecturer (tenure-track position) in the Department of Pure Mathematics at the University of New South Wales (UNSW) in SydneyI 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...view more

Since July 2018 I am a Lecturer (tenure-track position) in the Department of Pure Mathematics at the University of New South Wales (UNSW) in SydneyI 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.

 


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.


Currently supervising

  • Fev. 2019--Present. Co-supervisor (together with Ian Doust) of Allan Stoneham for his Ph.D. thesis.
  • June 2020--April 2021. Supervisor of Ryan Seelig for his Honours thesis.
  • Fev. 2020--Dec. 2020. Supervisor of  Christian de Nicola Larsen for his Honours thesis.

My Engagement

  • April 2020--Present. Contributing editor of the online magazine Parabola published by the School of Mathematics and Statistics of UNSW in partnership with the Australian Mathematics Trust.
  • March 2020--Present. Organiser of the Pure Math Seminar at UNSW.
  • March 2020--Present. 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--Present. 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

  • 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