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Preparatory Course PDF Print E-mail

 

In preparation of the Conference on Conformal Field Theory, Autormorphic Forms and Related Topics there will be a preparatory course, taking place July 11 - 22 at the Mathematics Department. The lectures will cover subjects on modular forms, vertex operators, denominator formula and relation to conformal field theory. This will give an introduction to the mathematical techniques which are underlying the topics of the CFT conference. The target audiences are postdocs and mathematical graduate students with a previous knowledge in modular forms. The course will enable them to participate and take advantage of the conference lectures.

 

The speakers are:

 

Miranda Cheng (Harvard University):

General Title: Automorphic Forms in String Theory and Geometry

Abstract:

In this set of lectures I will summarize the fruitful interplay between physics and the subject of automorphic forms. On the one hand, the latter has found many applications in physics, and in particular in string theory. On the other hand, I will demonstrate how string theory provides a natural connection between various automorphic forms and between automorphic forms and geometry. The topics that we will cover include :

1) the relation between Elliptic Genus and Jacobi Forms,

2) the relation between Automorphic Forms, Generalised Kac-Moody Algebras, and String Theory Black Holes.

If time permits, we will also cover some more advanced topics including

3) Modular AdS/CFT: the relation between Rademacher Sums and Three-Dimensional Gravity

4) Mock Modular Forms and Physics

 

 

Geoffrey Mason (University of California, Santa Cruz):

General title: Vertex operator algebras and modular-invariance.

Abstract:

These talks are an introduction to vertex operator algebras (VOAs) and the relations between VOAs, their automorphism groups, and modular forms. Topics include:

the Monster simple group, hauptmoduln and the modular function j; Borcherds/Jacobi identity and locality of quantum fields; axiomatics of VOAs; Virasoro, Heisenberg and affine Kac-Moody algebras; lattice theories; representations of VOAs; rational VOAs, $1$-point functions and Zhu's modular-invariance theorem; Jacobi forms in VOA theory; automorphisms of a VOA and twisted representations; modular-invariance of twisted representations; construction of the Moonshine module.

 

Schedule
Date Time
Speaker
Location

Tuesday  07-12-2011

16:00 - 17:30

Mason

HS 2

Wednesday 07-13-2011

14:00 - 15:30

Mason

HS 2

Friday 07-15-2011

14:00 - 15:30

Mason

HS 3

Tuesday 07-19 -2011

16:00 - 17:30

Cheng

HS 2

Wednesday 07-20-201

14:00 - 15:30

Mason

HS 2

Thursday 07-21-2011

14:00 - 15:30

Cheng

HS 2

Friday 07-22-2011

14:00 - 15:30

Cheng

HS 3

Last Updated on Sunday, 31 July 2011 22:29