July 20, 2012
Extended higher Chern-Simons theories
Posted by Urs Schreiber
We have been busy working on a little article. Now we feel it is time to show our current version around, before doing some last polishing and then posting it to the arXiv:
Domenico Fiorenza, Hisham Sati, Urs Schreiber,
Extended higher cup-product Chern-Simons theories
Check out section 1 Introduction and overview, for the story (6 pages). The rest is details.
I am grateful to the organizers of String-Math 2012 for providing an environment in which this was finalized.
July 19, 2012
Zero-Determinant Strategies in the Iterated Prisoner’s Dilemma
Posted by Mike Shulman
A note to those arriving from the article in the Chronicle of Higher Education: my opinion may not have been accurately represented in that article. Please read my whole post and judge for yourself.
Usually I blog about things because I am excited about them, but today is a little different. Not that I’m not excited about this post, but recently I’ve been too busy with other things to do much blogging. However, what excitement can’t do, annoyance can, and I’m getting tired of seeing this (amazing, surprising, insightful, groundbreaking) paper subject to hype and (what seems to me to be) misinterpretation.
- William Press and Freeman Dyson, Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent, PNAS open access, March 2012.
July 16, 2012
Notes from String-Math 2012
Posted by Urs Schreiber
This week I am in Bonn at String-Math 2012, the second in a new annual series of conferences on mathematical aspects of string theory (the first was in Philadelphia, last year).
I will post notes about some talks below in the comment section.
They will be a bit more terse than I originally intended, because at the same time I have to be finalizing an article with Hisham and Domencio, on Extended higher cup-product Chern-Simons theories before I go on vacation next week.
We’ll see how it works out. Now on to Frenkel’s talk…
July 10, 2012
Morton and Vicary on the Categorified Heisenberg Algebra
Posted by John Baez
Wow! It’s here!
- Jeffrey Morton and Jamie Vicary, The Categorified Heisenberg Algebra I: A Combinatorial Representation.
July 9, 2012
Geometric Quantization on Moduli ∞-Stacks
Posted by Urs Schreiber
I am on the train to Higher Structures VI in Göttingen, doing last touches on my talk handout
Higher geometric prerequantization on moduli infinity-stacks
talk handout pdf (4 pages) .
I have mentioned this before. Here is a quick idea of what this is about:
There are two formalizations of the notion of quantization: geometric quantization and algebraic (deformation) quantization. The latter is naturally formulated in higher algebra in terms of ∞-cosheaves. The former should have a natural formulation in higher geometry, in terms of ∞-sheaves = ∞-stacks. Aspects of a formulation of such higher geometric quantization over smooth manifolds have been introduced and studied by Chris Rogers, see the references listed here. Examples like the following suggest that this is usefully generalized to higher geometric quantization over ∞-stacks in general and moduli ∞-stacks of higher gauge fields in particular.
For, write for the smooth moduli stack of G-connections, for a simply connected simple Lie group, and write for the smooth moduli -stack of n-form connections on smooth circle n-bundles ( bundle gerbes). Then, by FSS, there is an essentially unique morphism of smooth ∞-stacks
which refines the generating universal characteristic class , and this as the following properties: its transgression to the loop mapping stack of
modulates the -WZW-model B-field 2-bundle, its trangression to the mapping stack out of a compact oriented 2-dimensional manifold
restricts to the prequantum circle bundle of -Chern-Simons theory, and finally its transgression to the mapping stack out of a 3-dimensional
is the action functional of -Chern-Simons theory.
This suggests that we should regard itself as the prequantum circle 3-bundle of -Chern-Simons theory extended down to dimension 0.
What is a Hamiltonian vector field on a moduli stack such as ? What is the Poisson bracket -algebra? How does it act on prequantum 3-states? How to these trace/transgress to prequantum -states on ?
Answers to such questions I’ll indicate in my talk.