We discuss the strategies and results on the determination of index and nullity of minimal surfaces. In particular, we prove that for any large enough $m$, the genus $\gamma=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere in the round three-sphere, which has two catenoidal bridges at the poles and  $m$ bridges equidistributed along the equatorial circle and was discovered in earlier work of Kapouleas, has index $2g+5=2m+7$ and nullity $6$.  We also discuss the progress in the study of indices of minimal surfaces from similar constructions.

https://yale.zoom.us/j/92334178441?pwd=FmjkR0LeihzxyR7AaNzsvTIPa11tmK.1 [4]