# Associate Professor Scott Morrison

## Biography

I'm an ARC Future Fellow and Associate Professor at the Mathematical Sciences Institute of the Australian National University.

My research interests include Khovanov homology, derived topological quantum field theories (TQFTs), and small examples of subfactors and singly generated tensor categories. More details can be found on my research page, or my lists of publications and talks.

From 2009-2012, I was a Miller Fellow at the UC Berkeley mathematics department During 2007-2009, I was a postdoc at Microsoft Station Q, at UC Santa Barbara.

I completed my Ph.D. in March 2007 at the University of California, Berkeley, studying with Vaughan Jones. My thesis received the Herbert Alexander Prize for Outstanding Dissertation in Pure Mathematics. Before Berkeley, I graduated from the University of New South Wales, Australia, with first class honours and the University Medal in pure mathematics.

## Publications

- Constructing spoke subfactors using the jellyfish algorithm. Joint with David Penneys. Available at http://arxiv.org/abs/1208.3637.
- The little desert? Some subfactors with index in the interval (5,3+\sqrt{5}). Joint with Emily Peters. Available at http://arxiv.org/abs/1205.2742
- Higher categories, colimits and the blob complex. Joint with Kevin Walker, Proceedings of the National Academy of Sciences May 17, 2011 vol. 108 no. 20 pp. 8139-8145.
- Subfactors of index less than 5, part 3: quadruple points. Joint with Masaki Izumi, Vaughan Jones and Noah Snyder, accepted at Communications in Mathematical Physics, October 8 2011.
- Cyclotomic integers, fusion categories, and subfactors. Joint with Frank Calegari and Noah Snyder, Communications in Mathematical Physics Volume 303, Issue 3 (2011), pp. 845-896.
- Knot polynomial identities and quantum group coincidences. Joint with Emily Peters and Noah Snyder, Quantum Topology vol. 2 (2011), pp. 101--156.
- Non-cyclotomic fusion categories. Joint with Noah Snyder, in press at Transactions of the American Mathematical Society.
- Subfactors of index less than 5, part 1: the principal graph odometer. Joint with Noah Snyder, accepted at Communications in Mathematical Physics, June 28 2011.
- Subfactors of index less than 5, part 2: triple points. Joint with David Penneys, Emily Peters and Noah Snyder, International Journal of Mathematics Vol. 23, No. 3 (2012) 1250016 (33 pages).
- The blob complex. Joint with Kevin Walker, in press at Geometry & Topology.
- Constructing the extended Haagerup planar algebra. Joint with Stephen Bigelow, Emily Peters and Noah Snyder, in press at Acta Mathematica.
- Man and machine thinking about the smooth 4-dimensional Poincare conjecture. Joint with Michael Freedman, Robert Gompf and Kevin Walker, Quantum Topology, Volume 1, Issue 2 (2010), pp. 171--208.
- The braid group surjects onto G_2 tensor space. Pacific Journal of Mathematics 249-1 (2011), pp. 189-198.
- Skein theory for the D_{2n} planar algebras. Joint with Emily Peters and Noah Snyder, Journal of Pure and Applied Algebra Vol. 214, No. 2 (2010) pp. 117-139.
- Fixing the functoriality of Khovanov homology. Joint with David Clark and Kevin Walker, Geometry and Topology 13 (2009) pp. 1499-1582.
- On Khovanov's cobordism theory for su_3 knot homology. Joint with Ari Nieh, Journal of Knot Theory and its Ramifications Vol. 17, No. 9 (2008), pp. 1121-1173.
- The Karoubi Envelope and Lee's Degeneration of Khovanov Homology. Joint with Dror Bar-Natan, Algebraic & Geometric Topology 6 (2006) pp. 1459-1469.

## Projects and Grants

Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.

- Quantum Symmetries: mathematical models for topological matter (Primary Investigator)
- Low dimensional categories (Primary Investigator)
- Symmetries of subfactors (Primary Investigator)
- Fusion categories and topological quantum field theory (Primary Investigator)