Exceptional structures in geometry and field theory

4 Mar 2013, 10:00 → 8 Mar 2013, 16:30 Asia/Tokyo

Lecture hall (1st floor), Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo

The aim of this winter school is to bring together researchers and students interested in the study of exceptional structures in geometry and physics. Historically fruitful examples of exceptional algebraic structures have included the E-series of simple Lie algebras, the Leech lattice, and the monster simple group. The discovery of each of these has led to new understanding of representation theory and the structure of fundamental physics, such as orbifold conformal field theory. We will focus on new efforts at classification, including recent work on fusion categories and hyperbolic Lie algebras, and on specific structures, such as the conjectural Mathieu symmetry underlying superconformal field theories attached to K3 surfaces. There is funding available, provided by the University of Tsukuba "Program to disseminate the Tenure Tracking System". Please request funding when registering.

Organizers

• Scott Carnahan
• Satoshi Kondo
• Kyoji Saito

Speakers

• Daniel Allcock (UT Austin)
• Miranda Cheng (Jussieu)
• John Duncan (Case Western Reserve University)
• Scott Morrison (Australian National University)
• Noah Snyder (Indiana University)
• Hiroshi Yamauchi (Tokyo Women's Christian University)

Titles

• Allcock: Root systems for rank 3 hyperbolic Kac-Moody algebras
• Cheng: Umbral moonshine
• Duncan: Umbral Moonshine
• Morrison: Constructing and classifying small subfactors
• Snyder: Dualizable Tensor Categories
• Yamauchi: Binary codes and classification of framed vertex operator algebras

Monday 4 March

Noah Snyder: Dualizable Tensor Categories (1)

11:00 Break

Scott Morrison: Constructing and classifying small subfactors (1)

12:30 Lunch

Daniel Allcock: Root systems for rank 3 hyperbolic Kac-Moody algebras (1)

15:00 Tea

Miranda Cheng: Umbral moonshine (1)

Tuesday 5 March

Miranda Cheng: Umbral moonshine (2)

11:00 Break

John Duncan: Umbral Moonshine (1)

12:30 Lunch

Discussion

Wednesday 6 March

John Duncan: Umbral moonshine (2)

11:00 Break

Noah Snyder: Dualizable Tensor Categories (2)

12:30 Lunch

Scott Morrison: Constructing and classifying small subfactors (2)

15:00 Break

Miranda Cheng: Umbral moonshine (3)

Thursday 7 March

Daniel Allcock: Root systems for rank 3 hyperbolic Kac-Moody algebras (2)

11:00 Break

Noah Snyder: Dualizable Tensor Categories (3)

12:30 Lunch

Hiroshi Yamauchi: Binary codes and classification of framed vertex operator algebras

15:00 Break

Scott Morrison: Constructing and classifying small subfactors (3)

16:30 Break

John Duncan: Umbral moonshine (3)

Friday 8 March

Daniel Allcock: Root systems for rank 3 hyperbolic Kac-Moody algebras (3)

11:00 Break

Noah Snyder: Dualizable Tensor Categories (4)

12:30 Lunch

Scott Morrison: Constructing and classifying small subfactors (4)

15:00 Break

Daniel Allcock: Root systems for rank 3 hyperbolic Kac-Moody algebras (4)