[geometry-ml:01520] Seminar at Kavli IPMU on 2012 August 7 Fuchs

[Satoshi Kondo]

Dear colleagues:

There will be a series of talks as follows at Kavli IPMU
(Kavli Institute for the Physics and Mathematics of
the Universe).

Regards,

Satoshi Kondo (Kavli IPMU)
http://ipmu.jp/
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Speaker:Jürgen Fuchs (Karlstad U)

Date: 2012 August 7 (tue)
Talk 1: 1:30 p.m. --- 3:00 p.m.
Talk 2: 3:30 p.m. --- 5:00 p.m.

Talk1:
Correlation functions in conformal field theory

Abstract:

I will review basic properties of correlation functions in conformal
field theory. This includes in particular a description of the
relation between correlation functions and conformal blocks (the
principle of holomorphic factorization), the sewing constraints and
mapping class group invariance, and a discussion of similarities and
differences between rational and logarithmic conformal field theories.
I will also summarize some pertinent features of the so-called
TFT-approch, which furnishes a universal construction of all
correlation functions (as elements of spaces of conformal blocks) of
rational CFTs by expressing them as invariants of three-manifolds with
embedded ribbon
graphs.


Talk 2:
Mapping class group invariants from factorizable Hopf algebras

Abstract:

I will describe the representation theory of finite-dimensional
factorizable ribbon Hopf algebras H as a laboratory for studying
aspects of logarithmic conformal field theories.
In particular, certain H-bimodules F and K play the role of the space
of bulk states and of the so-called bulk handle Hopf algebra of the
CFT, while bimodule morphisms involving these two objects correspond
to correlation functions of bulk fields.
The object F has a natural structure of a commutative symmetric
Frobenius algebra and is naturally a K-module. With the help of these
structures one can explicitly construct candidates for the morphisms
which play the role bulk field correlators
on closed surfaces of any genus and show that they are invariant under
the relevant action of the mapping class group.
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You can check the location from
http://www.ipmu.jp/access-0
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/