Assistant Operator Los Angeles Research .Net Software

Miller Fellow **** Evans Hall, University of California, Berkeley, CA 94720

+1-805-***-**** *****@****.*** http://tqft.net/

Scott Morrison - Resume

Employment

Miller Fellowship, UC Berkeley.

July 2009-present. I am a Miller Fellow at UC Berkeley, in the mathematics department. Please

see my research statement for a description of my current interests.

Post-doctoral research, Microsoft Station Q.

April 2007-June 2009. Station Q is a multidisciplinary research group, focusing on topological quan-

tum computing. The research interests of the group cover condensed matter physics, especially

topological phases and the fractional quantum hall e ect, and quantum topology, a eld of

mathematics describing topological quantum eld theories (TQFTs) and their applications.

During my stay at Station Q, my research was primarily on extensions of TQFT which in-

troduce ideas from homological algebra, and on the classi cation of TQFTs related to von

Neumann algebras and quantum groups.

Education

University of California, Berkeley, Doctor of Philosophy (Mathematics).

2001-2007. Worked with Prof. Vaughan Jones. Received the 2007 Herbert Alexander Prize for

Outstanding Dissertation in Pure Mathematics. Received the Outstanding Graduate Student

Instructor Award, 2004.

University of New South Wales, Bachelor of Science (Hons.)

1998-2001, Sydney, Australia. First class honours in Mathematics, and the University Medal.

Publications

2010

The blob complex

Joint with Kevin Walker. Submitted to Geometry & Topology, available at arXiv:1009.5025.

Subfactors of index less than 5, part 2: quadratic tangles and triple points

Joint with David Penneys, Emily Peters and Noah Snyder. Available at arXiv:1007.2240.

Subfactors of index less than 5, part 1: the principal graph odometer

Joint with Noah Snyder. Available at arXiv:1007.1730.

Cyclotomic integers, fusion categories, and subfactors

Joint with Frank Calegari and Noah Snyder, with an appendix by Victor Ostrik. To appear

Communications in Mathematical Physics, available at arXiv:1004.0665.

Knot polynomial identities and quantum group coincidences

Joint with Emily Peters and Noah Snyder. To appear Quantum Topology, available at arXiv:1003.0022.

Non-cyclotomic fusion categories

Joint with Noah Snyder. To appear Transactions of the American Mathematical Society, available

at arXiv:1002.0168.

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2009

Constructing the extended Haagerup planar algebra

Joint with Stephen Bigelow, Emily Peters and Noah Snyder. To appear Acta Mathematica, available

at arXiv:0909.4099.

Man and machine thinking about the smooth 4-dimensional Poincar conjecture

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Joint with Michael Freedman, Robert Gompf and Kevin Walker, Quantum Topology, Volume 1,

Issue 2 (2010), pp. 171208. Available at arXiv:0906.5177.

The braid group surjects onto G2 tensor space

In press Paci c Journal of Mathematics, available at arXiv:0907.0256.

2008 and earlier

Skein theory for the D2n planar algebras

Joint with Emily Peters and Noah Snyder, Journal of Pure and Applied Algebra Vol. 214, No. 2

(2010) pp. 117-139. Available at DOI:10.1016/j.jpaa.2009.04.010 or arXiv:0808.0764.

A Diagrammatic Category for the Representation Theory of Uq (sln )

Ph.D. thesis, available at arXiv:0704.1503.

Fixing the functoriality of Khovanov homology

Joint with David Clark and Kevin Walker, Geometry and Topology 13-200*-****-****. Available

at DOI:10.2140/gt.2009.13.1499 or arXiv:math.GT/0701339.

On Khovanov s cobordism theory for su3 knot homology

Joint with Ari Nieh, Journal of Knot Theory and its Rami cations Vol. 17, No. 9 (2008). Available

at DOI:10.1142/S0218216508006555 or arXiv:math.GT/0612754

The Karoubi Envelope and Lee s Degeneration of Khovanov Homology

Joint with Dror Bar-Natan, Algebraic & Geometric Topology 6-200*-****-****. Available at

DOI:10.2140/agt.2006.6.1459 or arXiv:math.GT/0606542.

Classifying Spinor Structures

BSc. honours thesis at UNSW. Available at arXiv:math-ph/0106007.

Outreach

I m a co-founder and moderator of MathOver ow, a website for mathematicians to ask and an-

swer research-level questions. MathOver ow is just over a year old, receives approximately 10000

visits each day, and the 9000 users ask or answer about 30 new questions each day. With Anton

Geraschenko and Ravi Vakil, I wrote an opinion piece about MathOver ow for the June 2010 issue

of the Notices of the AMS.

Software

FusionAtlas

A Mathematica package for analysing subfactors and fusion categories, with contributions by David

Penneys, Emily Peters, Noah Snyder and James Tener. Available online.

Omath

A free implementation of the core Mathematica langauge, joint with Joseph Farjoun. Available

from http://omath.org.

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QuantumGroups

A Mathematica package for the representation theory of quantum groups, including quantum knot

invariants. Available online with a brief tutorial in arXiv:1003.0022.

KnotTheory and the Knot Atlas

A Mathematica package for knot theory, co-maintained with Dror Bar-Natan, with contributions

from many people. Available from the Knot Atlas.

Conferences

Quantum Topology in Wellington

With David Gauld, I organised the Quantum Topology session of a joint NZMS/AMS meeting in

Wellington, New Zealand, December 2007.

Subfactors in Maui

I organised a conference on subfactors and topology in Maui, July 2007.

Teaching

University of California, Berkeley

Outstanding Graduate Student Instructor Award, 2004. Teaching Assistant for 9 semesters, for

MATH 1B (Introductory Calculus), 53 (Multivariable Calculus), 54 (Linear Algebra), 53H

(Honors), 54H (Honors), 110 (Linear Algebra), and 121A (Mathematical Methods for the

Physical Sciences).

University of New South Wales

Tutor ( Teaching Assistant ) for 2 semesters, introductory calculus.

My current teaching statement is available online.

Selected talks

Classi cation of subfactors to index 5

UCLA/DARPA subfactors meeting, Subfactors at index 5 and beyond, October 8

2010. (slides)

Quantum groups, Clermont-Ferrand, September 2 2010.

Operator algebras satellite conference, Chennai, August 11 2010.

Non-commutative geometry and operator algebras, Vanderbilt, May 11 2010. (slides)

Fusion Categories at AMS Waco meeting, Fusion categories and small index subfac-

tors, October 18 2009. (slides)

UC Berkeley Colloquium, Fusion categories, September 3 2009. (blackboards)

UC Riverside Colloquium, Classifying subfactor planar algebras, June 3 2009.

Blob Homology

Low dimensional topology and categori cation, Stony Brook, June 23 2010. (slides)

TQFT and link homology in Hahei, January 18 2010.

Homotopy Theory and Higher Algebraic Structures at AMS Riverside meeting, November

8 2009. (slides and video)

Los Angeles Joint Topology Seminar, October 9 2009.

UC Riverside, June 3 2009.

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AMS Annual meeting, Washington DC, January 6 2009. (slides)

Georgia Topology Conference, May 15 2008.

Extended Haagerup

Tensor Categories in Bloomington, Indiana, Extended Haagerup exists!, March 22

2009. (slides, video and blog post)

Coincidences of tensor categories

Quantum Invariants of 3-manifolds and Modular Categories at St Paul AMS meeting,

April 10 2010.

Algebraic Structures in Knot Theory at AMS Riverside meeting, November 7 2009.

(slides)

The Cappell-Shaneson spheres and the s-invariant

Knots in Washington January 9 2009. (slides)

UC San Diego, topology seminar, December 4 2008. (slides)

Skein theory for the D2n subfactors

University of Tokyo operator algebras seminar, October 16 2008.

University of New South Wales, pure mathematics seminar, October 7 2008.

Pennsylvannia State University, noncommutative geometry seminar, September 16 2008.

Planar Algebras and Subfactors at Vanderbilt, April 18-20 2008.

Khovanov Homology

Introduction

MSRI introductory workshop for the link homology semester, January 25-26 2010.

Khovanov homology II, functoriality, deformations and the s-invariant (lecture notes,

streaming video, video) and Khovanov homology I (lecture notes, streaming video,

video)

Local Khovanov Homology, Workshop on Geometric Methods in the Topology of 3-

Dimensional Manifolds (NZ Mathematics Research Institute), Taipa, New Zealand,

January 2006. (slides)

Functoriality

Functoriality and duality in Khovanov homology, Kyoto, May 23 2007. (notes)

Columbia, gauge theory seminar, November 17 2006. (slides)

Invited speaker at Categori cation in Algebra and Topology, Uppsala, September

7-10, 2006. (slides)

Park City Mathematics Institute, July 3 2006. (slides)

Knots in Washington, May 6 2006. (slides)

4-manifold TQFT invariants

TQFT and link homology in Hahei, January 17 2010

Quantum Topology Special Session of the joint NZMS/AMS Wellington meeting,

December 12-15 2007. (slides)

Quantum Topology in Hanoi, Vietnam, August 6-10 2007. (slides)

Oporto conference on Link Homology, Portugal, July 5-8 2007. (slides)

Rational tangles

AMS Annual meeting, Washington DC, January 8 2009. (slides)

SU(3)

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A topological categori cation of su3, University of Oregon colloquium, December

4 2006. (slides)

A cobordism theory for sl3 knot homology, UCSB, topology seminar, April 11

2006. (slides)

Genus bounds

Genus bounds and spectral sequences made easy Kyoto, May 15 2007. (slides)

UC Davis Student Topology Seminar, February 22 2007.

UC Berkeley Topology Seminar, February 21 2007.

UT Austin Winter School on Knot Theory and Representations, January 11-14 2007.

Spiders for Uq (sln )

Station Q Seminar, UC Santa Barbara, October 2 2007. (slides)

University of Cologne, algebra seminar, November 2005.

Quantum Topology AMS Meeting, Snowbird, Utah, June 2005. (slides)

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