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Abstracts for Spring School: Characters of Representations and Modular Forms

Alternatively have a look at the program.

Characters of representations of Lie (super)algebras and (mock)theta functions

Posted in
Speaker: 
V. Kac
Datum: 
Die, 24/03/2015 - 09:00 - 10:15
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms

Prerequisits:
Understanding of the Weyl character formula, universal enveloping algebra and Verma modules.
Knowledge of some elements of Lie superalgebra theory.
Knowledge of some elements of Jacobi theta functions and modular forms.
Programm:
1. Lie superalgebras
2. Ane Lie (super)algebras: loop and KM constructions
3. Character formula for integrable and admissible representations in the Lie algebra case and Jacobi
theta functions
4. Character formula for tame integrable and admissible modules in the Lie superalgebra case and
mock theta functions

Modular and quasimodular forms, partitions, and representations of symmetric groups

Posted in
Speaker: 
D. Zagier
Datum: 
Die, 24/03/2015 - 10:45 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms 
In 1995, Robbert Dijkgraaf found a "mirror symmetry in dimension one"
statement saying that the generating function counting genus g ramified
coverings of a torus was what is now called a quasimodular form on the
full modular group (i.e., a polynomial in the Eisenstein series E_2,
E_4 and E_6) of weight 2g-2. A mathematical proof of this was given
by Kaneko and myself in a small paper in which we also gave the
definition and basic properties of quasimodular forms.

Characters of representations of Lie (super)algebras and (mock)theta functions

Posted in
Speaker: 
V. Kac
Datum: 
Mit, 25/03/2015 - 09:00 - 10:15
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms

Prerequisits:
Understanding of the Weyl character formula, universal enveloping algebra and Verma modules.
Knowledge of some elements of Lie superalgebra theory.
Knowledge of some elements of Jacobi theta functions and modular forms.
Programm:
1. Lie superalgebras
2. Ane Lie (super)algebras: loop and KM constructions
3. Character formula for integrable and admissible representations in the Lie algebra case and Jacobi
theta functions
4. Character formula for tame integrable and admissible modules in the Lie superalgebra case and
mock theta functions

Mock theta functions and representation theory of affine Lie superalgebras and superconformal algebras

Posted in
Speaker: 
M. Wakimoto
Datum: 
Mit, 25/03/2015 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms

One of the beautiful properties in representation theory of ane Lie
algebras is the SL2pZq-invariance of the space of characters of integrable modules
discovered by Kac-Peterson in the early 1980's.
However, for ane Lie superalgebras, modular invariance had long been quite un-
clear except for only a few cases. Recently a remarkable breakthrough was brought
by Zwegers, who constructed a modular function from the supercharacter of the
ane slp2|1q-module of level 1 by adding non-holomorphic correction term, which
is called the "modi cation" procedure.

Characters of representations of Lie (super)algebras and (mock)theta functions

Posted in
Speaker: 
V. Kac
Datum: 
Don, 26/03/2015 - 09:00 - 10:15
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms

Prerequisits:
Understanding of the Weyl character formula, universal enveloping algebra and Verma modules.
Knowledge of some elements of Lie superalgebra theory.
Knowledge of some elements of Jacobi theta functions and modular forms.
Programm:
1. Lie superalgebras
2. Ane Lie (super)algebras: loop and KM constructions
3. Character formula for integrable and admissible representations in the Lie algebra case and Jacobi
theta functions
4. Character formula for tame integrable and admissible modules in the Lie superalgebra case and
mock theta functions

Modular-invariance in rational conformal field theory: past, present and future

Posted in
Speaker: 
G. Mason
Datum: 
Fre, 27/03/2015 - 10:45 - 11:45
Location: 
MPIM Lecture Hall
Parent event: 
Spring School: Characters of Representations and Modular Forms

This is a tentative outline of my two lectures. No prior knowledge of vertex
rings is assumed, though the foundations will be covered only sketchily due to
time constraints. The main purpose of the lectures is to explain how modularity
enters into VOA theory, and to discuss an approach to the general problem of
modular-invariance in rational CFT based on a theory of vector-valued modular
forms, Fuchsian systems, and the Riemann-Hilbert problem.
Optional background reading on VOAs:
U. Heidelberg, downloadable lecture notes on connections between VOAs and the

 

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