Dan's Notes (access required):

 Nathan Seiberg on QFT:

Some Expository Writing:

 Popular Introductions to Topological Phases:

On Bordism:

On Symmetry and QFT:

State of the Art:

There is a research conference at Perimeter Institute which includes some talks (Gaiotto, Fuchs) related to the content of the workshop:

Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics

Perimeter posts videos of the talks as they conclude.