This is the first talk in the Emory-Ga Tech-UGA joint seminar. The second talk will begin at 5:00. (NOTE: These talks are on the UGA campus.)
I will survey the program of realizing various versions of Floer homology as a theory of geometric cycles. This involves the description of infinite dimensional manifolds mapping to the relevant configuration spaces. This approach, which goes back to Atiyah's address at the Herman Weyl symposium, is in some ways technically simpler than the traditional construction based on Floer's version of Morse theory. In addition, it opens up the possibility of defining more refined invariants such as bordism andK-theory.