Abstract: A famous conjecture of Yongbin Ruan says that quantum cohomology of birational varieties becomes isomorphic after analytic continuation when the birational transformation preserves the canonical class (the so-called crepant transformation). When the transformation is not crepant, the quantum cohomology becomes non-isomorphic, but it is conjectured that one side is a direct summand of the other. 

In this talk, I will explain a conjecture that a semiorthogonal decomposition of topological K-groups (or derived categories) should induce a relationship between quantum cohomology. The relationship between quantum cohomology can be described in terms of solutions to a Riemann-Hilbert problem.

Seminar note：https://www.math.kyoto-u.ac.jp/~iritani/talk_QC_birat.pdf