In “en espérant que je ne me rende pas compte de son absence.”
We have “rendre” in the subjunctive as “rende”. This has been triggered by “espérer que”. But I thought that an affirmative use of “espérer que” would use the Indicative as opposed to the Subjunctive. I don’t know what additional implication the use of the gerund has though…
https://www.lawlessfrench.com/subjunctivisor/esperer/