## February 27, 2006

### Kapranov and Ganter on 2-Characters

#### Posted by Urs Schreiber

In

Nora Ganter & Mikhail Kapranov
*Representation and Character Theory in 2-Categories*

math.KT/0602510

an interesting relation between a notion of trace for lax group representations and various known phenomena all somehow related to *equivariant string theory* are established.

## February 23, 2006

### Graphs, Operads and Renormalization

#### Posted by Urs Schreiber

While I won’t do justice to the title of this entry, I do want to record a neat relation between these three items which I recently came across while browsing some literature.

**Update:** See the update at the end of this entry.

## February 17, 2006

### On Transport Theory

#### Posted by Urs Schreiber

On Wed., Feb. 22, 18:00 there will be a talk (Hamburg math department)

**Abstract:**

$n$-transports are an $n$-functors describing

$\bullet$ parallel trasport in $n$-bundles

$\bullet$ propagation in $n$-dimensional QFT.We describe basic notions of $n$-transport theory, such as trivialization, transition and trace and discuss examples.

This is a synthesis of the material contained in [I, II, III, IV, V, VI].

## February 12, 2006

### 1st Northern German String workshop

#### Posted by Urs Schreiber

Hamburg’s recently founded center for mathematical physics hosts the

**1st Northern German String workshop**

Feb 13 - Feb 14

DESY seminar room 2, building 2a

$\to$program

$\to$participants

**Update:** Robert has written something about this meeting. I won’t.

## February 9, 2006

### Problemi Attuali di Fisica Teorica 06

#### Posted by Urs Schreiber

This year’s conference in the annual series *Problemi Attuali di Fisica Teorica* will be held April 7 - April 13 in Vietri, Italy (like last year).

### Workshop on Gerbes, Groupoids and QFT

#### Posted by Urs Schreiber

In the context of an ESI program on *Gerbes, Groupoids and Quantum Field Theory* there will be a workshop in Vienna from May 9 to May 13 2006.

Official application deadline was a couple of days ago, but one can still apply.

## February 8, 2006

### FRS Reviews

#### Posted by Urs Schreiber

Two new reviewes of (aspects of) the Fuchs-Runkel-Schweigert (“FRS”) approach to conformal field theory have recently appeared:

C. Schweigert, J. Fuchs & I. Runkel
*Categorification and correlation functions in conformal field theory*

math.CT/0602079

and

C. Schweigert, J. Fuchs & I. Runkel
*Twining characters and Picard groups in rational conformal field theory*

math.QA/0602077 .

The first of these was, incidentally, also the basis for the colloquium talk preceeding the one on 2-vector bundles and elliptic cohomology which I mentioned recently. I conjecture that there is more to this conjunction of talks than meets the eye.

As introductions to the motivation and logic of FRS, I can stronly recommend the following texts

I. Runkel
*Algebra in Braided Tensor Categories and Conformal Field Theory*

pdf

I. Runkel, J. Fjelstad, J. Fuchs, Ch. Schweigert
*Topological and conformal field theory as Frobenius algebras*

math.CT/0512076.

J. Fuchs, I. Runkel & C. Schweigert
*Open Strings and 3D Topological Field Theory*

pdf

The full details can be found in this series of papers

J. Fuchs, I. Runkel, Ch. Schweigert
*TFT construction of RCFT correlators I: Partition functions
*

hep-th/0204148

J. Fuchs, I. Runkel, Ch. Schweigert
*TFT construction of RCFT correlators II: Unoriented world sheets*

hep-th/0306164

J. Fuchs, I. Runkel, Ch. Schweigert
*TFT construction of RCFT correlators III: Simple currents
*

hep-th/0403157

J. Fuchs, I. Runkel, Ch. Schweigert
*TFT construction of RCFT correlators IV: Structure constants and correlation functions*

hep-th/0412290

J. Fuchs, I. Runkel, Ch. Schweigert
*TFT construction of RCFT correlators V: Proof of modular invariance and factorisation*

hep-th/0503194

### Special Ambidextrous Adjunctions

#### Posted by Urs Schreiber

## February 7, 2006

### Philosophy of Real Mathematics

#### Posted by Urs Schreiber

While I am struggling to understand elliptic cohomolohy, David Corfield, over on his weblog, has taken a look at the literature from the perspective of a philosopher of *real* mathematics.

“Real” here is meant in the sense of “what active mathematicians are *really* concerned with”, as opposed to an eternal occupation with Russel’s paradox and Gödel’s incompleteness. Have a look at his book for more.

To me, the interesting point to be addressed here is how we actually go about identifying the structures that we feel should be out there. As in: “How should we really think about elliptic cohomology?”, or the outworn but still curiously elusive “What *is* string theory?”. And maybe this one: “Is there a relation between these two questions?”

## February 6, 2006

### Lauda & Pfeiffer on Open-Closed Topological Strings, II

#### Posted by Urs Schreiber

A while ago I had mentioned Aaron Lauda and Hendryk Pfeiffer’s work on open/closed topological strings. Now there is a followup

A. Lauda & H. Pfeiffer
**State sum construction of two-dimensional open-closed Topological Quantum Field Theories**

math.QA/0602047.

## February 5, 2006

### Seminar on 2-Vector Bundles and Elliptic Cohomology, IV

#### Posted by Urs Schreiber

Transcript of part 3 of our first session.

### Seminar on 2-Vector Bundles and Elliptic Cohomology, III

#### Posted by Urs Schreiber

Transcript of part 2 of our first session.

## February 3, 2006

### Seminar on 2-Vector Bundles and Elliptic Cohomology, II

#### Posted by Urs Schreiber

Here is a transcript of part 1 of our first session.

## February 2, 2006

### Seminar on 2-Vector Bundles and Elliptic Cohomology, I

#### Posted by Urs Schreiber

We currently have a series of seminars here on tensor categories and their application in CFT. After having heard talks about the basics of tensor categories and the way they appear in the FRS formalism of CFT, today Birgit Richter gave an introductory review of the work

N. Baas, B. Dundas & J. Rognes
**Two-vector bundles and forms of elliptic cohomology**

math.AT/0306027

which I surely have mentioned several times before here at the coffee table.

I’ll try to give a transcript of what was going on today. More meetings on this topic are planned and should go into deeper details.

Here, I’ll start with what, to me at least, is the bird’s eye perspective on the entire program.

### Exploring the Blogosphere

#### Posted by Urs Schreiber

As noted already elsewhere in the blogosphere (by P.P. Cook and by P. Woit) there are currently a couple of acticles concerned with math and physics blogging.

In his article Exploring the Blogosphere, Craig Laughton, who runs the blog Gooseania says, to my mind, some very true things about the *benefits of blogging*.

I use this opportunity to remind the (potential) readers of any of these blogs once again that the way to read blogs without becoming insane is to use an RSS reader software. The latest Mozialla Thunderbird has one built in.

### Orbifold String Topology: Paths in Smooth Categories

#### Posted by Urs Schreiber

Motivated by I. Moerdijk’s remarks I began studying

E. Lupercio, B. Uribe & M. Xicoténcatl
**Orbifold String Topology**

math.AT/0512658

with the honest intent to write something about this. But one main concept used in this work is a notion of loop space of an orbifold, expressed in groupoid language as the **loop groupoid**, and it turned out that I had my own ideas on this object. Thinking about this interfered with my intent to read the rest of the paper. So in order to get this out of the way first I here present instead some observations on an alternative perspective on the loop groupoid.

So here are some notes:

## February 1, 2006

### Moerdijk on Orbifolds, III

#### Posted by Urs Schreiber

Here is the trascript of the second talk. (The first one was discussed here.)

As I mentioned before, most of what was said in this talk can be found in

I. Moerdijk

**Orbifolds as Groupoids: an Introduction**

math.DG/0203100.

I’ll try to report on more recent developments concerning loop spaces of orbiolds (loop orbifolds, actually) in a seperate entry.