For a HER2 positive patient who has undergone neoadjuvant HER2-directed therapy, do you offer adjuvant trastuzumab if the surgical specimen is HER2 negative?   

I still would give trastuzumab for a year. The neoadjuvant thereapy may have destroyed the Her2 positive clones in the breast, but there still could be micromets distantly that are Her2 positive.

Conversion to HER2 negativity has been reported as high as 28% of cases."Loss of HER2 and disease prognosis after neoadjuvant treatment of HER2+ breast cancer" (Branco FP et al., Am J Transl Res 2019)