** Speaker:** Andrei Okounkov (Columbia University)

** Title:** Relative vs. descendent insertions in quasimap counting

** Abstract:**A much studied problem in enumerative geometry (in particular, in Donaldson-Thomas theory) is to develop a dictionary between different ways to impose an incidence constraint on a sheaf or a quasimap. I will explain recent progress achieved in enumerative K-theory of quasimaps to Nakajima varieties and, in particular, Hilbert schemes of ADE surfaces (which is the part that is relevant to K-theoretic DT theory of threefolds). Two slightly different dictionaries were established first by Smirnov, and later by Aganagic and the speaker.