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I will discuss some of the basic structure of Chern-Simons theory with complex gauge group (in particular, gauge group SL(2,C)). This is a complex, noncompact analogue of the Chern-Simons theory famously studied by Witten in relation to Jones polynomials. It leads to new quantum 3-manifold invariants intrinsically related to hyperbolic geometry, which can be explicitly computed given (say) sufficiently nice ideal triangulations. Some of these invariants were recently found to be related to normal surface theory. The invariants also appear to come with a natural categorification, via a physical idea known as the 3d-3d Correspondence.

Pease note that we start 10 minutes earlier than usually.