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I've begun putting all the videos of my talks up at youtube.

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2020

• February 13, Interactive Theorem Proving, Berkeley Colloquium. (slides) (video)
• February 3/5, The blob complex, MSRI Quantum Symmetries program. (slides part 1 part 2)

2019

• August 16, Theorem proving for mathematicians, Joint MSI/RSCS seminar. (video)
• July 1-5, Planar algebras and fusion categories, Lecture series at the Quantum Symmetries research school, Bogota. (notes)
• June 5, Interactive theorem proving and category theory, Quantum Symmetries summer school, Ohio State. (video)
• May 3, Higher dimensional algebras, Noncommutative Geometry and Operator Algebras, Vanderbilt. (slides) (video)
• April 12, Quantum probability, quantum mathematics seminar. (slides) (video)

2018

• October 10, Experiments in Lean, ANU Logic Seminar. (notes) (video)
• October 5, Interactive theorem proving, Adelaide Colloquium. (notes) (video)
• October 5, Exotic quantum symmetries, Adelaide Differential Geometry Seminar. (notes) (video)
• August 23, Automatic rewriting in Lean, Dagstuhl seminar on Formalization of Mathematics in Type Theory. (video) (report)
• April 18, Quantum probability, ANU Undergraduate Colloquium. (slides) (video)
• March 5, Khovanov homology as a 4-category, Quantum Knot Homology and Supersymmetric Gauge Theories, Aspen Center for Physics. (slides)
• January 9, 10, 12, Higher categories and topological matter, ANU Summer School on Topological Matter. (slides)

2017

• December 15, Quasistrict 3-categories, quantum mathematics seminar.
• October 13, Algebras in higher categories, and tensor networks, quantum mathematics seminar.
• October 10, Categories generated by a trivalent vertex, ANU Algebra and Topology seminar (slides) (video)
• July 18, Monoidal categories enriched in braided monoidal categories, Subfactors in Maui. (slides)
• May 26, The quantum exceptional series, Quantum mathematics seminar, ANU.
• January 31, Subfactors and Link Homology, 'Operator algebras and subfactors' and 'Link homology and low-dimensional topology' programs at the Isaac Newton Institute. (slides) (video)

2016

• December 15, The modular data machine, Interactions between topological recursion, modularity, quantum invariants, and low-dimensional topology, MATRIX. (slides)
• December 6, Monoidal categories enriched in braided monoidal categories, Algebraic topology, K-theory, and category theory special session at the AustMS annual meeting. (slides)
• November 4, LYMPH-TOFU, Kauffman, and ...?, Low-dimensional topology and quantum algebra conference at ANU. (slides)
• October 11, The modular data machine, Algebra and Topology Seminar, ANU. (slides)
• August 18, The modular data machine, Modular tensor categories, Oaxaca. (slides, video, article)
• May, The modular data for the extended Haagerup subfactor, Non-commutative geometry and operators algebras workshop, Bonn. (abstract, slides, article) Although we do not yet have a complete description of the centre of the extended Haagerup subfactor, in joint work with Terry Gannon and with Kevin Walker we have now computed the modular data (that is, the S and T matrices). These can be derived using a combination of combinatorial, Galois theoretic, and representation theoretic methods. We have also found that there are "healthy looking" vector valued modular forms associated to these S and T matrices.
• April 19, Quantum probability, a talk for the ANU Mathematics Society. (abstract, slides) I explain all of quantum mechanics, from scratch. This story is usually kept a secret, only revealed to the initiated few who can explain why a von Neumann algebra has a Banach space pre-dual. I'm not really sure why that is the case, and will boldly attempt to explain how you really should think about quantum mechanics, using only two-by-two matrices. I'll introduce non-commutative probability, mention Bell's theorem (and Bayes' theorem), and explain why "wave function collapse" is not anything scary and new.
• April 1, 8, Modular Tensor Categories, quantum mathematics seminar, ANU. (slides on the rank 2 classification)
• February 3, Topological field theory and fusion categories, Sydney Quantum Information Theory Workshop. (slides, video)

2015

• December 1, A gentle introduction to topological field theory, ANU summer research scholar program. (slides)
• November 23, The centre of extended Haagerup, Kioloa workshop. (slides)
• September 30, Quantum symmetries, AustMS medal talk, AustMS meeting at Flinders. (slides, video, citation)
  Medal citation:

  Scott Morrison was awarded his PhD in 2007 from the University of California at Berkeley and commenced a continuing position at the ANU in 2012.

  Scott’s research revolves around low-dimensional and quantum topology, and he has made fundamental contributions to link cohomology, subfactors and fusion categories, higher-dimensional homological algebra, and diagrammatic representation theory. In both blob homology, and the classification of subfactors and their indices, he has begun new fields involving many mathematicians world-wide. Perhaps his most striking work is in subfactor theory, in which he has brought breakthrough ideas and results, spearheading an effort with various collaborators and significantly increasing the variety of methods. This has resulted in the solution of problems of seemingly impossible complexity involving the characterisation of low index subfactors.

  Scott publishes in the very best mathematics journals (such as Acta Math). He is considered a leader in his fields, and has collaborated with the very best, including two Fields Medalists (Vaughan Jones and Michael Freedman). In recognition of his research, he was awarded the 2015 Christopher Heyde Medal from the Australian Academy of Science.

  Scott is a co-founder and moderator of MathOverflow, which has become the leading website where top experts in many fields of mathematics ask and answer questions (receiving about 10,000 hits daily). It is seen as a game changer in the way current and future mathematicians conduct their research.

• September 29, A quantum exceptional series, Representation theory and algebraic geometry session, AustMS meeting at Flinders. (abstract, slides)
  Abstract:

  Deligne has proposed a one-parameter family of tensor categories, which at special points recovers the representation categories of the exceptional simple Lie algebras. It's still unknown if these categories are well defined at other points, however. In joint work with Noah Snyder and Dylan Thurston, I've recently been studying a potential two-parameter family of tensor categories, recovering the quantum representation categories of the exceptional Lie algebras along certain curves. We still can't resolve the central problem: are these categories well-defined? Nevertheless there's some interesting new evidence, including candidate two-variable knot invariants.

• June 3, Fusion categories, Microsoft Station Q seminar, Santa Barbara.
• May 27, Topological matter, Christopher Heyde medal talk, Science at the Shine Dome. (abstract, slides, video)
  Abstract:

  Topology is a field of pure mathematics concerned with the shapes of things, without measuring lengths, angles, or areas. The standard joke is that a topologist can't tell the difference between a coffee mug and a donut.

  What could this have to do with real world physics? Recent discoveries in condensed matter physics reveal that certain exotic phases of matter are described by 'topological field theories'.

  A topological field theory has an alternate description as a 'higher category', which is an algebraic gadget in which the algebraic operations are indexed by the ways we can glue topological shapes together.

  Dr Morrison studies and attempts to classify, topological field theories. They turn out to be most interesting in dimensions 2, 3, and 4 --— and whether or not that's a coincidence, those are the dimensions that matter in our world.

• May 14, Computation, quantum mechanics, and topology, MSI Friends and Alumni lecture. (abstract, slides, video)
  Abstract:

  Building quantum computers is a fundamental challenge for this century. Quantum computers offer a new paradigm of computation, offering amazing speed-ups for certain classes of problems. So far there aren't many problems where quantum computers are known to do better than classical computers, but there's a very important one --- the simulation of other quantum systems, for example superconductors or photosynthesis!

  Building a quantum computer is seriously difficult! But it's so important, that it's worthwhile to explore ambitious, and perhaps crazy, solutions. One such potential solution is "topological quantum computation". This is based on the recent discovery of "topological phases of matter", exotic condensed matter systems that display topological symmetry. I study mathematical models of topological phases of matter, with the goal of classifying examples and discovering interesting new ones.
  

  I'll explain what a quantum computer is meant to look like, and how we might be able to use a topological phase of matter to build one.

• May 11, Topological quantum computation, and tensor categories, University of Queensland mathematics colloquium. (abstract, slides, video)

  Abstract: I'll explain the connection between quantum computation and topology, by analysing the computational complexity of the Jones polynomial. Recent discoveries in condensed matter physics potentially give us the tools to build quantum computers based on topological field theories. My research on topological field theories and the algebraic structures underlying them, particularly tensor categories and fusion categories, helps us understand which topological field theories may be accessible to experiment and engineering, and which can support quantum computation.

• April 14, Topological quantum computation, and tensor categories, Peking University topology seminar. (slides)
• March 24, Small examples: subfactors and fusion categories, Oberwolfach workshop on subfactors and conformal field theory. (notes)
• January 27, Exotic fusion categories, IPAM workshop on symmetries and topological matter. (notes, video)

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2014

• December 12, Small trivalent categories, Representation theory session of the AustMS annual conference. (notes, video)
• July 17, Evaluation algorithms, Subfactors in Maui. (notes)
• May 5,7,8, Problems in the classification of small index subfactors, NCGOA 2014, Vanderbilt. (abstract, notes, videos: part 1 part 2 part 3)

  Abstract: There's recently been quite a bit of progress on classifying small index subfactors. I'll explain the general problem, and the overall framework as employed in the successful classification of subfactors with index less than 5 (besides those with trivial standard invariant). Since then, there have been four major advances: results by Liu on the presence of intermediate subfactors, results of Penneys and Bigelow on "stable" principal graphs, results of Penneys extending Jones work on quadratic tangles to obtain new obstructions, and an implementation by Afzaly of a much faster principal graph enumerator, based on the isomorph-free generation techniques of McKay. I'll give an update on where we now stand, and give special attention to the outstanding problems in pushing classifications even further.

• April 15, How the classification of small index subfactors works, Banff workshop on Subfactors and Fusion Categories. Joint talk with Noah Snyder. (video: part 1 part 2)
• February 20, Progress on fusion categories, Modern Trends in Topological Quantum Field Theory, Erwin Schrödinger Institute, Vienna. (abstract, slides, video)

  Abstract: The 2-dimensional extended TFTs correspond to fusion categories. We know constructions of fusion categories from finite group data and from quantum groups at roots of unity, but what else is out there? We are very far from having satisfying answers, but have now approached the problem from several different directions. I will explain some of the notions of a 'small' fusion category, and describe what we've seen so far. Some examples, in particular the fusion categories coming from the Haagerup subfactor, appear over and over again. I suspect that 'eventually' there will be an unmanageable surfeit of sporadic fusion categories, but so far efforts at classification have turned up surprisingly few instances.

• January 28, Topological quantum computation, lunch time talk for the AMSI summer school at ANU. (slides, video)

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2013

• December 9, The $x$-colour theorems, at Representation Theory at the Beach. (slides)
• November 6, Khovanov homology and 4-manifolds, Representation Theory in Geometry, Topology and Combinatorics, University of Melbourne. (abstract, slides, video)

  Abstract: I'll begin by describing the Jones polynomial (and more generally, knot invariants coming from quantum groups) in terms of a 3-category, and explain how we extract invariants of low-dimensional manifolds using this category. Then I'll explain how to describe Khovanov homology (a categorification of the Jones polynomial) in terms of a 4-category, and outline what this might tell us about 4-manifolds.

• September 6, The Jones polynomial and quantum computation, University of Adelaide colloquium. (abstract, slides, audio)

  Abstract: I'll begin with the Jones polynomial, a knot invariant discovered 30 years ago that radically changed our view of topology. From there, we'll visit the complexity of evaluating the Jones polynomial, the topological field theories related to the Jones polynomial, and how all these ideas come together to offer an unorthodox model for quantum computation.

• September 6, What are fusion categories?, University of Adelaide differential geometry seminar. (abstract, notes, audio)

  Abstract: Fusion categories are a common generalization of finite groups and quantum groups at roots of unity. I'll explain a little of their structure, mention their applications (to topological field theory and quantum computing), and then explore the ways in which they are in general similar to, or different from, the 'classical' cases. We've only just started exploring, and don't yet know what the exotic examples we've discovered signify about the landscape ahead.

• August 13, The quantum exceptional trefoil, ANU algebra seminar. (notes)
• July 15, Trivalent graphs, Subfactors in Maui. (notes, video)
• July 3, Subfactors, planar algebras, and fusion categories, Category Theory and its Applications, Macquarie University. (notes, video: part 1 part 2 part 3 part 4)
• May 14, Webs and skew Howe duality, Quantum Topology in Nha Trang, Vietnam. notes)
• March 8, Constructing exotic examples, Exceptional structures in geometry and field theory, Kashiwa IPMU, Tokyo. (notes)
• March 7, Classification in small regimes, Exceptional structures in geometry and field theory, Kashiwa IPMU, Tokyo. (notes)
• March 5, The planar algebra toolkit, and examples, Exceptional structures in geometry and field theory, Kashiwa IPMU, Tokyo. (notes)
• March 4, Subfactors and planar algebras, Exceptional structures in geometry and field theory, Kashiwa IPMU, Tokyo. (notes)
• February 11, Khovanov homology as a 4-category, ANU/Macquarie category theory workshop. (notes)

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2012

• November 16, Khovanov homology and 4-manifolds, Northwestern geometry/physics seminar. (abstract, notes for pre-talk)

  Abstract: I'll describe our attempts to define Khovanov homology for 4-manifolds. We beginning by constructing a `disklike 4-category' from Khovanov homology. There are certain technical difficulties, and for now we're forced to work in characteristic 2. From there, we follow the standard topological field theory recipe to construct vector space valued invariants of 4-manifolds (possibly with boundary, possibly with a link in the boundary). Along the way, however, this construction loses some of the nice properties of Khovanov homology, in particular the exact triangle for resolving a crossing in a link. Our recent work on the blob complex began as an attempt to remedy this defect, and I'll describe the computational tool that the blob complex provides in this context.

• November 15, Small fusion categories, Vanderbilt colloquium. (abstract, slides)

  Abstract: Over the last two decades our understanding of small index subfactors has improved substantially. We have discovered a slew of examples, some related to finite groups or quantum groups, and other `sporadic' examples. At present we have a complete classification of (hyperfinite) subfactors with index at most 5, and a few results that push past 5. I'll explain the main techniques behind these classification results, and also spend a little time describing how we construct the sporadic examples. (Joint work with many people!)

• November 14, Khovanov homology and 4-manifolds, Vanderbilt topology and group theory seminar. (notes, video)
• November 13, Webs and skew Howe duality, Vanderbilt subfactor seminar. (abstract, notes, video)

  Abstract: The representation category of SL(n) is a pivotal tensor category. This means that one can draw planar diagrams representing morphisms, with composition corresponding to vertical stacking, and tensor products corresponding to horizontal juxtaposition. Any planar isotopy of such a diagram gives equations between the corresponding morphisms. For any such category, we'd like to be able to give a presentation via certain generators modulo local relations. For Rep(SL(n)), we've had a conjectural presentation for several years, but no good tools for showing that we have all the relations. With Sabin Cautis and Joel Kamnitzer, we now have not only a proof that this presentation is correct, but also a clear conceptual explanation of how the relations arise. This explanation uses skew Howe duality.

• October 26, Knots and quantum computation, Wollongong colloquium. (abstract, slides, video)

  Abstract: I'll begin with the Jones polynomial, a knot invariant discovered 30 years ago that radically changed our view of topology. From there, we'll visit the complexity of evaluating the Jones polynomial, the topological quantum field theories related to the Jones polynomial, and how all these ideas come together to offer an unorthodox model for quantum computation.

• October 25, Subfactors as quantum symmetries, Operator Algebra seminar at Wollongong. (abstract, notes, video)

  Abstract: I'll explain how every finite group $G$ can be realized (essentially uniquely) as outer automorphisms of the hyperfinite $II_1$ factor $R$. Taking the fixed points we obtain a subfactor $R^G \subset R$. From the representation theory of $R^G \subset R$ we can recover the group $G$. A useful perspective on subfactors is to think of any subfactor $A \subset B$ as arising in this way from a `quantum symmetry group'. We're still exploring this new world: constructing new examples, understanding just how `exotic' these are, and proving classification results in some regimes. I'll tell you what we've seen so far.

• September 27, The search for small fusion categories, Plenary talk at the AustMS annual meeting at Ballarat. (abstract, slides)

  Abstract: Fusion categories are a beautiful generalization of finite groups and quantum groups. A fusion category is the essential underlying algebraic data of a topological field theory in 2+1 dimensions. Over the past decade and a half, we've been trying to understand the small examples of fusion categories. I'll touch on the connections with group theory, category theory, condensed matter phyiscs and operator algebra, and show you some of the most interesting examples. Recent work has revealed that there are surprisingly few such examples, making the ones we have all the more precious!

• September 22, Higher categories, lower manifolds, Early Career Workshop at the AustMS annual meeting. (abstract, slides)

  Abstract: I've been interested in the interplay between category theory and topology, especially through topological field theory. To tell manifolds apart, we want to compute invariants. Sometime, these invariants can be computed by cutting the manifold into smaller pieces, computing something "algebraic" associated to each piece, then assembling the pieces via some algebraic rules. The theory of higher categories is more or less the theory of possible ways to assemble algebraic data associated to small pieces of manifolds. I'll tell you about some of the aspects of this problem that I've worked on, and how I ended up working on them!

• September 21, The blob complex, Algebra/Geometry/Topology Seminar at the University of Melbourne. (abstract, notes, video)

  Abstract: Topological field theories associate vector spaces to n-manifolds (and sometimes numbers to (n+1)-manifolds, although that won't concern us much). The blob complex provides a natural way to see these vector spaces as the 0-th homology of an invariant chain complex. I'll explain some nice properties of this chain complex, and tell you what we might hope to learn about manifolds by looking at the higher homologies of this chain complex.

• August 28, Khovanov homology for 4-manifolds and the blob complex, New Perspectives in Topological Field Theories, Hamburg. (notes, video)
• July 16, Turaev-Viro theory and connections, Subfactors in Maui. (notes)
• July 4, The blob complex, ANU. (notes)
• May 21, The blob complex, Stanford RT+QA/Topology seminar. (notes)
• March 14, Constructing exotic subfactors, AIM workshop on classifying small fusion categories.
• February 17, The $5-\epsilon$ colour conjecture, UC Berkeley subfactor seminar. (notes)
• January 31, A 4-manifold invariant from Khovanov homology, UC Davis geometry/topology seminar. (notes, video)
• January 25, Computing pushforwards of data sets, Amgen bio-informatics group.
• January 9, Can we get to $3+\sqrt{5}$?, Kyoto conference on von Neumann algebras. (rough notes)

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2011

• December 6, Knots and quantum computation, Miller Institute lunch talk. (video, slides)
• November 14, Khovanov homology and 4-manifold invariants, Eugene colloquium. (abstract, video, notes)

  Abstract: I'll describe an invariant of smooth 4-manifolds defined in terms of Khovanov homology. It associates a doubly-graded vector space to each 4-manifold (optionally with a link in its boundary), generalizing the Khovanov homology of a link in the boundary of the standard 4-ball. I'll finish by talking about relations to TQFT, and the prospects for concrete calculations. This is joint work with Chris Douglas and Kevin Walker.

• November 10, Invariants of 4-manifolds from Khovanov homology, Boston College. (video, slides)
• October 29, Connections and planar algebras, Von Neumann algebras and Conformal Field Theory at Vanderbilt. (abstract, handout)

  Abstract: With Emily Peters, I've been exploring subfactors with index in the interval $(5, 3+\sqrt{5})$. We've recently obtained a classification of 1-supertransitive subfactors in this range, and performed an extensive computer search in higher supertransitivities. I'll describe the examples of subfactors we've found. We have two main new techniques. First, even when we only know a fragment of a principal graph, we can extract certain inequalities by considering the norms of the entries of a connection. This allows the new classification result. Second, we extend the theory of bi-unitary connections to the bi-invertible case, and find we can then work over a fixed number field. This allows effective use of the "hybrid method" of constructing subfactors: given a not-necessarily flat bi-invertible connection, we can efficiently solve the equations for a flat element in the graph planar algebra. This lets us completely analyse the examples.

• October 21, The blob complex, Toronto. (abstract, video, Bar-Natan's notes)

  Abstract: In my paper with Kevin Walker, we defined the blob complex, which pairs an $n$-manifold and an $n$-category to produce a chain complex. When $n=1$ and the manifold is the circle, this is the Hochschild complex. Thus the blob complex is a generalization of Hochschild homology to higher dimensional algebraic structures, where we can specify the $n$-dimensional shape "along which" we compute. Alternatively, the $0$-th homology is the usual TQFT invariant. Thus we can think of the extra information in the chain complex as extending TQFT invariants in the same way that Hochschild homology extends the coinvariants of an algebra. I'll define the blob complex, sketch its important properties, and outline its intended applications, calculating invariants of manifolds based on exotic higher categories.

• October 19, Small index subfactors, Toronto colloquium. (abstract, slides)

  Abstract: Fusion categories provide a simple model for a collection of particles which can split and fuse. Despite the simplicity of the model, it has proved useful in describing exotic materials in condensed matter physics. On the mathematical side, fusion categories can be thought of as 'quantum' finite groups. I'll describe recent joint work on the classification of small fusion categories. The new examples we've encountered are rather strange objects. Moreover, the classification is much sparser than we had expected, encouraging the hope of extending our current knowledge to larger and larger classes of fusion categories. Along the way we'll use analysis (von Neumann algebras and subfactors), number theory (the geometry of cyclotomic integers), graph combinatorics, two-dimensional topology, and some representation theory!

• October 15, Invariants of 4-manifolds from Khovanov homology, Category-theoretic methods in representation theory, Ottawa. (abstract, slides, blog post)

  Abstract: I'll explain how to define invariants of 4-manifolds (possibly with boundary, possibly with a link in the boundary) from Khovanov homology. The construction relies on a new property of Khovanov homology, roughly 'S^3 functoriality'. I'll try to indicate where the difficulties may lie establishing this property for the variations of Khovanov homology based on categorified quantum groups other than SU(2). Finally, I'll explain how this construction is best viewed as a partial categorification of the 3+1 dimensional TQFT of which the usual Witten- Reshetikhin-Turaev theories are the boundary, rather than a direct categorification of a WRT theory.

• October 8, Classifying fusion categories and subfactors, SIAM Mini-symposium on Algebraic Aspects of Quantum Computing, Raleigh. (slides)
• July 22, The blob complex, Subfactors in Maui. (notes)
• July 21, The $5-\epsilon$ colour theorem., Subfactors in Maui.
• June 7, 4-manifold invariants from Khovanov homology, Michael Freedman's 60th Birthday Conference, Berkeley. (abstract, slides, video)

  Abstract: I'll describe an invariant of smooth 4-manifolds defined in terms of Khovanov homology. It associates a doubly-graded vector space to each 4-manifold (optionally with a link in its boundary), generalizing the Khovanov homology of a link in the boundary of the standard 4-ball. For now, we can only make the construction in characteristic two. I'll finish by talking about relations to TQFT, and the prospects for concrete calculations. This is joint work with Chris Douglas and Kevin Walker.

• May 24, 4-manifold invariants from Khovanov homology, Stanford topology seminar. (abstract, slides, slides)

  Abstract: I'll show you the topological quantum field theory recipe for defining invariants of n-manifolds from a ``disklike n-category'', illustrated by the particular example of Khovanov homology. Unfortunately, there's still a gap in our knowledge --- we don't yet know that our attempts to construct a disklike 4-category from Khovanov homology really satisfies all the requisite axioms. I'll carefully explain this defect and what remains to be done before we can build invariants of arbitrary 4-manifolds via this recipe.

• May 20, Classifying small index subfactors, Great Plains Operator Theory Symposium. (slides, slides)
• February 9 and 16, Topological field theory and the blob complex, University of Sydney and the Australian National University. (abstract, notes)

  Abstract: An n-dimensional topological field theory (TFT) associates vector spaces to n-manifolds, and higher algebraic data to lower dimensional manifolds. In the optimal situation, a TFT associates an n-category to the point (the 0-dimensional manifold), and this n-category in fact determines the entire TFT, via gluing formulas. I'll describe an extension of this framework, which we call the "blob complex". The blob complex associates a chain complex to each n-manifold, whose 0-th homology is the usual TFT vector space. When n=1, TFTs are essentially determined by associative *-algebras, and the blob complex for the circle is equivalent to the Hochschild complex of the algebra. Thus we have a generalization of Hochschild homology to higher dimensions which at the same time extends the usual TFT invariants. The blob complex satisfies certain "A-infinity gluing formulas", which suggest connections to important new invariants of manifolds coming from Seiberg-Witten theory, Heegard-Floer theory, and Khovanov homology. This is joint work with Kevin Walker.

• January 25, February 1, Field and local relations, Teichner's hot topics course on the blob complex. (notes)
• January 21, Khovanov homology for 4-manifolds, GRASP seminar UC Berkeley. (notes)
• January 13, Fusion categories and subfactors, UCSD Colloquium. (slides, slides)

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2010

• November 10, Fusion categories and subfactors, Caltech Colloquium. (slides, slides)
• October 29, Classifying subfactors up to index 5, Kyoto Operator Algebra seminar. (slides)
• October 8, Subfactors at index 5 and beyond, UCLA/DARPA subfactors meeting. (slides)
• September 2, Classification of subfactors up to index 5. Quantum groups, Clermont-Ferrand. (slides)
• August 11, Classification of subfactors up to index 5. Operator algebras satellite conference, Chennai (slides)
• June 23, The blob complex. Low dimensional topology and categorification, Stony Brook. (slides, video)
• June 4, Classifying fusion categories. Miller Institute Symposium. (poster)
• May 11, Classification of subfactors up to index 5., Non-commutative geometry and operator algebras, Vanderbilt. (slides)
• April 10, Coincidences of small modular tensor categories related to the D_2n planar algebra Quantum Invariants of 3-manifolds and Modular Categories session of the St Paul AMS meeting. (abstract)

  Abstract: I'll quickly describe the D_2n planar algebra, and using this discover some coincidences between small modular tensor categories. One example is that (G_2)_{1/3} is isomorphic to the even part of D_{14}, proving that it is unitary. These coincidences give new identities between quantum knot polynomials.

• January 26, Khovanov homology II, functoriality, deformations and the s-invariant, MSRI introductory workshop for the link homology semester. (lecture notes, video, video (alternate))
• January 25, Khovanov homology I, MSRI introductory workshop for the link homology semester. (lecture notes, video, video (alternate))
• January 18, Blob homology, TQFT and link homology in Hahei.
• January 17, Khovanov homology for 4-manifolds, TQFT and link homology in Hahei.

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2009

• November 8, Blob homology, part I, special session on Homotopy Theory and Higher Algebraic Structures at AMS Riverside meeting. (slides, video)
  • see also slides and video from part II, by Kevin Walker.
• November 7, Coincidences of tensor categories, special session on Algebraic Structures in Knot Theory at AMS Riverside meeting. (slides)
• October 30, Graph planar algebra embedding theorems, subfactor seminar at UC Berkeley.
• October 18, Fusion categories and small index subfactors, part II, special session on Fusion Categories at AMS Waco meeting. (slides)
  • see also slides from part I, by Noah Snyder.
• October 9, Blob homology, Los Angeles Joint Topology Seminar.
• September 3, Fusion categories, UC Berkeley Colloquium. (blackboards)
• June 3, Classifying subfactor planar algebras, UC Riverside colloquium.
• June 3, Blob homology, UC Riverside.
• March 22, Extended Haagerup exists!, Tensor Categories in Bloomington, Indiana. (slides, video and blog post)
  • see also March 20, Coincidences of tensor categories, at the same conference, a talk given by Noah Snyder on joint work. (slides and blog post)
• January 9, The Cappell-Shaneson spheres and the s-invariant, Knots in Washington. (slides)
• January 8, Blob homology, AMS Washington meeting. (slides)
• January 6, Khovanov homology of rational tangles, AMS Washington meeting. (slides)

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2008

• December 4, The Cappell-Shaneson spheres and the s-invariant, UC San Diego. (slides)
• October 16, The D_2n planar algebras, University of Tokyo.
• October 7, The D_2n planar algebras, University of New South Wales seminar.
• September 26, Generators and relations for U_q(sl_n) as a pivotal category, University of Sydney algebra seminar.
• September 16, The D_2n planar algebras, PennState noncommutative geometry and analysis seminar.
• July 8, Introduction to Khovanov homology and genus bounds for links, Station Q seminar.
• May 15, Blob homology, Georgia Topology Conference.
• April 18-20, Skein theory for the D_2n subfactors, Planar Algebras and Subfactors meeting at Vanderbilt.
• February 1, Link invariants from the D4 subfactor, with Emily Peters and Noah Snyder, UC Berkeley subfactor seminar.

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2007

• December 12-15, Lasagna composition for Khovanov Homology, in the Quantum Topology Special Session of the joint NZMS/AMS Wellington meeting. (slides)
• October 2, Spiders for U_q(sl_n), Station Q Seminar, UC Santa Barbara. (slides)
• August 6-10, Lasagna composition for Khovanov Homology, Quantum Topology in Hanoi, Vietnam (slides)
• July 5-8, Lasagna composition for Khovanov Homology, Oporto conference on Link Homology, Portugal (slides)
• May 23, Functoriality and duality in Khovanov homology, Kyoto. (Nakajima's notes, photos)
• May 15, Genus bounds and spectral sequences made easy, Kyoto. (slides)
• May 14, Khovanov homology, Kyoto. (slides)
• April 24, Khovanov homology is functorial in S^3, Braids In Banff. (slides)
• February 21 and 22, Rasmussen's genus bounds from Khovanov homology, UC Berkeley and UC Davis topology seminars.

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2006

• December 4, A topological categorification of su_3, Colloquium, University of Oregon, Eugene. (slides)
• December 1, Khovanov Homology, Basic Notions Seminar, University of Oregon, Eugene. (slides)
• November 17, Disoriented and confused: fixing the functoriality of Khovanov homology. Columbia, Gauge Theory Seminar. (slides, handout.)
• September 7, Disoriented and confused: fixing the functoriality of Khovanov homology. Uppsala, Categorification in Algebra and Topology. (slides, handout.) My slides got a mention at the n-Category Cafe.
• July 3, Disoriented and confused: fixing the functoriality of Khovanov homology. PCMI. (slides)
• June 16, A cobordism theory for sl_3 knot homology, Subfactor seminar.
• May 6, Disoriented and confused: fixing the functoriality of Khovanov homology. Knots in Washington. (slides, handout, actual handout)
• April 28, Disoriented and confused: fixing the functoriality of Khovanov homology. (slides)
• April 11, A cobordism theory for sl_3 knot homology (slides, handout), UCSB topology seminar.
• Khovanov Homology, Taipa conference Jan 2006. (slides)

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2005

• Spiders and Gelfand-Tsetlin bases, University of Cologne, November 23, (abstract)

  Abstract: Spiders, invented by Kuperberg, are a combinatorial and graphical model for the representation theory of a (complex, simple) Lie algebra. (You might have heard some other names for pretty much the same things -- 'planar categories', 'pivotal categories', or 'planar algebras'.) Kuperberg described the generators and relations for the spiders corresponding to each of the rank 2 Lie algebras, A_2, B_2 and G_2. I can tell you about a construction using Gelfand-Tsetlin bases which allows us to get a handle on the spiders of each A_n. Using this, I'll show you a finitely presented spider which is conjecturally equivalent to the category of representations of U_q(sl_n). Hopefully, I'll have time to tell you exactly what is missing before this becomes a theorem!

• omath, UC Berkeley Subfactor seminar.
• The Knot Atlas, at Knots in Washington.
• Bar-Natan's local Khovanov homology, UC Berkeley Subfactor seminar.
  • Abstracts June 30, July 7 (there was a 3rd talk on September 9, also).
  • You can download my slides from the first two talks and my slides from the 'delooping' talk.
• Generators and relations for $Rep(U_q(\mathfrak{sl}_n))$ as a pivotal category.
  • Abstracts February 11, February 18.
  • I gave a short 25 minute version of this talk at the Quantum Topology AMS meeting at Snowbird, in June. You can download overheads as an ~8mb pdf.

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2004

• Pivotal categories, planar algebras and subfactors
  • Abstracts October 15, October 29, November 5.

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2002

• October 25, The Temperley-Lieb algebra and $\mathfrak{sl}_2$ representation theory, UC Berkeley subfactor seminar. (abstract)
• October 11, Jones-Wenzl projections in the Temperley-Lieb algebra, UC Berkeley subfactor seminar. (abstract)
• May 8, Juggling for Geeks, Many Cheerful Facts graduate seminar. (abstract)

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2001

• June 8, Classifying Spinor Structures, honours talk at the University of New South Wales. (abstract)

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