Hodge numbers of a hypothetical complex structure on S6

These are the notes for the talk “Hodge numbers of a hypothetical complex structure on S6” given by the author at the MAM1 “(Non)-existence of complex structures on S6” held in Marburg in March 2017. They are based on [12] and [27], where Hodge numbers and the dimensions of the successive pages of the Frölicher spectral sequence for S6 endowed with a hypothetical complex structure are investigated. We also add results from [20], where the Bott-Chern cohomology of hypothetical complex structures on S6 is studied. The material is not intended to be original.