Semisimple Quantum Cohomology and Blow-ups
  Using results of Gathmann, we prove the following theorem: If a smooth projective variety X has generically semisimple (p,p)-quantum cohomology, then the same is true for the blow-up of X at any number of points. This a successful test for a modified version of Dubrovin's conjecture from the ICM 1998. 
Arend Bayer (Max-Planck-Institut fuer Mathematik, Bonn)