Tensor Categories and Field Theory

Welcome to the information site for the upcoming seminar on tensor categories and field theory at the University of Melbourne, from June 5-9, 2017.

The recent years have seen a rich cross-fertilisation of ideas between physics and mathematics that has led to fantastic advances in each field. A prominent example of this is the notion of a tensor category. These abstract structures have a depth and ubiquity that has made them indispensable knowledge for many modern research fields including conformal field theory and vertex algebras, knot theory, operator algebras and subfactors, quantum groups, representation theory, topological quantum field theory and, more recently, applied fields such as condensed matter physics.

This workshop will bring together a dynamic mix of international experts from the mathematics and mathematical physics communities in order to disseminate this important work to graduate students and early career researchers through introductory lectures and research seminars.

Confirmed invited speakers and topics:

Gavin Brennen (Macquarie)

• Symmetric Tensor Networks as a tool to simulate particles and fields

Bianca Dittrich (Perimeter Institute)

• Lifting (2+1)D TQFT’s to (3+1)D theories with line defects (I and II).

Shashank Kanade (University of Alberta)

• Vertex tensor categories I: Fundamental constructions
• Vertex tensor categories II: Algebra objects and conformal embeddings

Liang Kong (University of New Hampshire)

• Boundary conformal field theories I: categorical description/classification
• Boundary conformal field theories II: applications to 2d topological orders

Dmitri Nikshych (University of New Hampshire)

• Braided fusion categories I: Basic theory and structure results
• Braided fusion categories II: Anisotropy and Witt equivalence

Eric Rowell (Texas A&M University)

• Modular Categories: Constructions, Conjectures and Classification
• Super-Modular Categories: Fermionic Quotients, Congruence Kernels and the 16-fold Way

Simon Wood (Cardiff University)

• Fusion by hand: The NGK algorithm

Organising committee:

Nora Ganter (University of Melbourne)

Pinhas Grossman (University of New South Wales)

Scott Morrison (Australian National University)

Thomas Quella (University of Melbourne)

Jorgen Rasmussen (University of Queensland)

David Ridout (University of Melbourne; Chair)