Introduction to TQFTs and Frobenius Algebras

Topological quantum field theories (TQFTs) are a type of quantum field 
theory that depend only on the topology of spacetime and so are a source 
of topological invariants. Much work has been done in trying to 
understand various types of TQFTs and the objects that classify them, 
most famously Lurie's proof of the cobordism hypothesis for fully 
extended TQFTs.

In this talk I will introduce everyone to the basics of TQFTs and the 
classical theorem that 2D TQFTs are classified by commutative Frobenius 
algebras. Time permitting I will also talk about extending TQFTs to 
lower dimensional submanifolds and how such theories can be determined 
by a small amount of data.