Floer homology theories have had an enormous impact on low-dimensional topology over the last 2-3 decades.  The goal of this talk is to introduce two Floer homology theories -- Heegaard Floer homology (due to Ozsvath-Szabo) and embedded contact homology (due to Hutchings) -- and to sketch a proof of the equivalence of the two.  This is joint work with Vincent Colin and Paolo Ghiggini.

The talk will be accessible to beginning graduate students.