Hiroshi Iritani: Decompositions of quantum cohomology under blowups

Abstract. It is an interesting question how (analytic continuation of) quantum cohomology is related to birational geometry. In particular, we expect that quantum cohomology decomposes in a certain way for extremal contractions. In this talk, I will explain such a decomposition for blowups: quantum cohomology of the blowup of X along Z will decompose into QH(X) and (codim Z-1) copies of QH(Z). The idea of the proof comes from Teleman's conjecture on quantum cohomology of symplectic reductions.