Subfactors group
From 4-8 February, the School of Mathematics and Statistics hosted the Subfactors in Sydney conference.

Invited presentations spanned a variety of topics in operator algebras, representation theory, conformal field theory, quantum computing, and group theory. In addition to the subfactor groups at UNSW and the Australian National University, there was also participation from the algebra and representation theory groups at University of Sydney and University of Melbourne. 

Talks were lively with most attracting multiple questions and comments from the audience. The workshop featured 20 speakers representing nine different countries. Nine speakers were Australia-based, and six speakers were Early Career Researchers (including our own Galina Levitina and Andrew Schopieray). 

Prof Freedman

Speakers included two US-based Fields Medallists, Professor Sir Vaughan Jones (Vanderbilt University) and Professor Michael Freedman (Microsoft Quantum - Santa Barbara). 

Subfactor theory was initiated in the 1980's by Professor Vaughan Jones as part of the theory of operator algebras. Operator algebras have been closely linked to mathematical physics since their introduction by Murray and von Neumann in the early twentieth century. Jones discovered a surprising link between subfactors and knots, which led to the formation of the new field of quantum topology.

In recent years, subfactor theory has developed connections to the theory of modular tensor categories. Modular Prof Jonestensor categories are used in mathematical models for topological quantum computing, an approach to quantum computation pioneered by Kitaev in the 1990's. One of the leaders in topological quantum computing is topologist Professor Michael Freedman, who heads a group working to build a quantum computer at Microsoft's Station Q in Santa Barabara. One of the themes of the workshop was the growing connection between subfactor theory and topological quantum computing.

Thank you to the conference organisers: Arnaud Brothier, Pinhas Grossman, Scott Morrison, Julia Plavnik, Andrew Schopieray and James Tener.
Thank you to our sponsors: AMSI; AustMS; UNSW School of Mathematics and Statistics. 

Pictured, clockwise from top: Conference participants; Prof Michael Freedman; Prof Vaughan Jones.