The three things I hope you will remember on Monday after my talk are:

1. From an operative point of view, links look much like functions, and if we knew how to integrate these functions, we'd have an invariant of 3-manifolds.

2. From an operative point of view, graphs look much like functions, and the calculus of Feynman diagrams allows us to "integrate" certain linear combinations of graphs.

3. Counting cosmic coincidences, we get a graph-valued invariant of links (and hence of 3-manifolds).

Prerequisites: You need to know what's a link, a manifold, a graph, and an integral. You don't need to know anything deep about these, though, and in particular, you don't need to know anything about Feynman diagrams. In fact, if you've never seen Feynman diagrams before and you are curious, today's your chance!

This abstract is at http://www.math.toronto.edu/~drorbn/Talks/GaTech-991203/.