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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:
-transports are an -functors describing
parallel trasport in -bundles
propagation in -dimensional QFT.We describe basic notions of -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
program
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.
Henri Matisse - La Gerbe
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.