## Conference on Higher Gauge Theory, Quantum Gravity, and Topological Field TheoryDecember 18, 2010

Posted by Chris Schommer-Pries in mathematical physics, QFT, quantum topology, talks, tqft, Uncategorized.
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In February there is going to be a workshop and school dedicated to exploring the interactions of Quantum Gravity, Higher Gauge Theory, and Topological Field Theory. I’m excited about the chance to share ideas and hopefully create some new mathematics.

The conference will take place in Lisbon, Portugal, and yours truly will be giving one of the mini-courses for the school (the topic is going to be the classification of extended 2D tqfts, something near and dear to my heart). Of course that makes me really excited, but I am also excited about the other topics too and I think the mix of ideas will be invigorating. For more info look below the break.

## Upcoming conference: Workshop on operator algebras and conformal field theory in EugeneMarch 30, 2010

Posted by Ben Webster in conferences, QFT.

I wanted to take a moment to plug a conference in my soon-to-be hometown Eugene, OR organized by my once and future colleague Nick Proudfoot.

Aside from Eugene being lovely in August, I felt this conference was worth a post because it’s something of a unique format. Rather than being a bunch of experts on the subject (as it says in the title, the subject is the conjunction of operator algebras and CFT) getting together and giving talks that only they understand, it will be aimed at being educational for graduate students and interested non-experts (such as myself). The format is a bit similar to that of Talbot. In particular, in addition to an organizer (Nick) it has a “leader” who is in charge of mathematical content (but will delegate quite a few of the lectures); that will be the incomparable Andre Henriques. (more…)

## Lurie on TFTsJanuary 15, 2009

Posted by Chris Schommer-Pries in Algebraic Topology, groupoids, QFT, tqft.

This morning Jacob Lurie posted a draft of an expository paper on his work (with Mike Hopkins) classifying extended (infinity, n)-categorical topological field theories and their relation to the Baez-Dolan cobordism hypothesis.

Should make for some intersting bedtime reading…

## TQFTs via Planar Algebras (Part 3)December 10, 2008

Posted by Chris Schommer-Pries in low-dimensional topology, Pictorial Algebra, planar algebras, QFT, quantum algebra, subfactors, talks, tqft.

This is the third and final post in my series about using planar algebras to construct TQFTs. In the first post we looked at the 2D case and came up with a master strategy for constructing TQFTs. In the last post we began carrying out that strategy in the 3-dimensional setting, but ran into some difficulties. In this post we will overcome those difficulties and build a TQFT.

## TQFTs via Planar Algebras (Part 2)December 6, 2008

Posted by Chris Schommer-Pries in low-dimensional topology, Pictorial Algebra, planar algebras, QFT, subfactors, talks, tqft.

In my last post I explained a strategy for using n-dimensional algebraic objects to construct (n+1)-dimensional TQFTs, and I went through the n=1 case: Showing how a semi-simple symmetric Frobenius algebra gives rise to a 2-dimensional TQFT. But then I had to disappear and go give my talk. I didn’t make it to the punchline, which is how planar algebras can give rise to 3D TQFTs!

In this post I will start explaining the 3D part of the talk. I won’t be able to finish before I run out of steam; that will have to wait for another post. But I will promise to use lots of pretty pictures!

## TQFTs via Planar AlgebrasDecember 5, 2008

Posted by Chris Schommer-Pries in low-dimensional topology, Pictorial Algebra, planar algebras, QFT, subfactors, talks, tqft.

So today I am giving a talk in the Subfactor seminar here at Berkeley, and I thought it might by nice to write my pre-talk notes here on the blog, rather then on pieces of paper destined for the recycling bin.

This talk is about how you can use Planar algebras planar techniques to construct 3D topological quantum field theories (TQFTs) and is supposed to be introductory. We’ve discussed planar algebras on this blog here and here.

So the first order of buisness: What is a TQFT?

## Symplectic duality slidesNovember 24, 2008

Posted by Ben Webster in Algebraic Geometry, category O, crazy ideas, link homology, mathematical physics, QFT, talks.

I’ve been too lazy to write in detail about the progress in my research (well, I am writing six papers and applying to jobs, so it isn’t entirely due to laziness), but I did recently speak in the symplectic seminar at MIT, and have posted the slides on my webpage. Obviously, they’re less useful without someone to explain them, but given the current lack of an overarching paper on the subject (that’s no. 5 on the list, I promise), I thought it might be edifying. Executive summary below the cut. (more…)

## Embedded TQFT?January 7, 2008

Posted by Ben Webster in Algebraic Topology, combinatorics, low-dimensional topology, QFT, topology, tqft.

So, a subject rather near and dear to the hearts of many of my fellow co-bloggers is that of 1+1-dimensional TQFT: that is, of monoidal functors from the category of 1-manifolds with morphisms given by smooth cobordisms to the category of vector spaces over your favorite field $k$.

There’s a rather remarkable theorem about such functors, which really deserves a post of its own for proper explanation, but I’ll spoil the surprise here.

Any such functor associates a vector space $A$ to a single circle, and to the “pair of pants” cobordism, it assigns a map $m:A\otimes A\to A$, which one can check is a commutative multiplication.

Furthermore, the cap, thought of as a cobordism from the empty set to a circle gives a map $i:k\to A$, which gives a unit of this algebra. Thought of as a cobordism from the circle to the empty set, it gives us a map $\mathrm{tr}:A\to k$ which we call the counit or Frobenius trace.

Theorem. A commutative algebra with counit $(A,\mathrm{tr})$ arises from a TQFT if and only if $\mathrm{tr}$ kills no left ideal of $A$.

## Witten: More on 3D gravityOctober 19, 2007

Posted by Scott Carnahan in differential geometry, low-dimensional topology, mathematical physics, QFT.