I am a PhD student working with a professor I do not know very well, as a proposed supervisor, on several postdoctoral applications. The professor's mother passed away several weeks ago. Since that point, I have been working on these applications independently, but I have determined that one of these applications will no longer be feasible, given some of the application requirements.
I am unsure whether I should very briefly update (and emphasize that no response/action is needed) this professor via e-mail so that they know that their workload is reduced during the coming months, or whether I should wait until they've reached out to me asking for an update. For context, we did not establish a date at which we would resume communication.
Any thoughts would be appreciated.