Oh, since the continuous "was speaking" is used, I can guess that the full context was something like: "He was speaking at the SETI conference, during a panel discussion about the Big Bang, when a baby alien suddenly punched its way out of his chest." (Or whatever happened while he was taking place in the panel discussion at the SETI conference.)

But my general remarks about "and", above, would still apply. You could say "A baby alien popped out of Filippenko's chest when he was speaking at a SETI conference in November 2011, and during a panel discussion in March 2012 -- seriously wounding him on the first occasion, but killing him the second time." But leaving out the "and" implies that the panel discussion was a part of the SETI conference.