[geometry-ml:01461] 5/26 Lectures on conformal field theory and related topics

[Satoshi Kondo]

Dear Colleagues,

Akihiro Tsuchiya was a starting member of IPMU in mathemtics and has
been a principal investigator in mathematics 2008-2011. He retired
from IPMU in March 2012.  We thank him for his contributions to start
mathematics at IPMU.  We plan to have his last lecture at IPMU as
follows. All are welcome.

Best,
Satoshi Kondo

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 Date:   May 26 (Sat), 2012
Place:   Seminar Room A, IPMU

Program:
13:30 - 15:00   Yoshitake Hashimoto (Tokyo City Univ.)
15:00 - 15:30   Tea break
15:30 - 17:00   Akihiro Tsuchiya
18:00 -         Dinner

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Title and Abstract.

************
Yoshitake Hashimoto (Tokyo City Univ.)

Title:
Conformal Field Theory Associated to C2-cofinite Vertex Operator Algebras
(joint with Professor Akihiro Tsuchiya)

Abstract:
   In this talk, we construct a sheaf of coinvariants on a base space
of families of stable curves associated to a C2-cofinite Vertex
Operator Algebra (VOA), and discuss the behavior of the sheaf for
degeneration of curves (factorization). We give a review on a VOA,
C2-cofiniteness, the Lie algebra and the associative algebra
associated to a VOA, and the regular bimodule.

************

Akihiro Tsuchiya

Title:  Extended W algebra of type A.D.E. at positive rational level

Abstract:  For each simple Lie algebra g and complex number κ, an
infinite dimensional algebra called W algebra, W_κ(g) were defined and
has been studied by many physicists and mathematicians. They have very
complicated algebraic structure and are discussed by the language of
Vertex operator algebras (V.O.A.). When g is sl_2(C), it gives the
Virasoro algebra.
   Recently the representation theory of these algebras are interested
by many mathematicians and physicists.
   I have been studied in the case of κ= p_−/p_+ positive rational
level, and g is of type A.D.E. Quite recently I got concrete results.
In these cases I found that these V.O.A. W_κ(g) can be extended in a
larger V.O.A. M_{p_+,p_−}(g). They are defined by compactified free
bosono and screening operators. These V.O.A. M_{p_+,p_−}(g) has very
nice structure and can be concretely analyzed.
In this talk, I will give their fundamental properties (some are conjectures).


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