Cain Edie-Michell

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I am a student at the Australian National University. I am working on a PhD in mathematics under the supervision of Scott Morrison. My research is in category theory and operator algebras. In particular I work with fusion categories, subfactors, and algebras constructed from topological groupoids. My thesis involves classifying pivotal fusion categories generated by objects of small dimension. This research is kindly supported by the Deakin PhD Scholarship and an ANU Supplementary Scholarship.

Publications

  • Uniqueness Theorems for Steinberg Algebras.
    joint with Lisa Orloff Clark, Journal of Algebras and Representation Theory, 18 (2015), 907-916
    ArXiv

Preprints

  • Equivalences of Graded Categories.
    ArXiv
  • A Field Guide to Categories with A_N Fusion Rules.
    joint with Scott Morrison.
    ArXiv
  • The Brauer-Picard Groups of the ADE Fusion Categories.
    ArXiv
  • Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras.
    joint with Lisa Orloff Clark, Astrid an Huef, and Aidan Sims.
    In press at the Transactions of the American Mathematical Society.
    ArXiv

Talks

  • October 2017, Planar algebras for the Drinfeld centres of the even parts of the ADE subfactors Vanderbilt Subfactor Seminar
  • September 2017, Planar Algebra Presentations for the Drinfeld Centres of PSU(2)_q UNSW Pure Mathematics Seminar
  • August 2017, An almost classication of fusion categories generated by a normal object of dimension less than 2 Special Session on Hopf Algebras and Tensor Categories at the XXII Coloquio Latinoamericano de Algebra in Quito
  • July 2017, Equivalences of Graded Categories Quantum Symmetries: Subfactors and Planar Algebras in Maui
  • June 2017, The Brauer-Picard groups of the ADE fusion categories Hopf Algebras and Tensor Categories in San Diego
  • March 2017, Natural Transformations for Planar Algebras ANU Quantum Mathematics Meeting
  • December 2016, The Brauer-Picard groups of the ADE fusion categories AustMS Annual Meeting
  • August 2016, Quantum Computing via Linear Algebra ANU Graduate Student Seminar
  • May 2016, The Brauer-Picard groups of the ADE fusion categories ANU Quantum Mathematics Meeting
  • November 2015, Classifying Quadratic Fusion Categories , Kioloa workshop.
  • March 2015 An Introduction to Topological Groupoid Algebras , ANU MSI graduate seminar.
  • October 2014, The Ideal Structure of Steinberg Algebras , honours talk at University of Otago.