On groping for the day

• "Carpe diem!" "Seize the day!"
• Great motto/slogan (although not one I have really practised, being an academic rather than a venture capitalist...)
• Still--it seemed like a good title for a blog post. Except that all my post headers seem to be in the form, "On..." (This was never a strategic decision, just a habit, but not one I feel inclined to break.)
• So! 'On "carpe diem"' ? That would work were I to be meditating on the phrase as such, but I'm actually going after the underlying sentiment. So I need to say something about "on Seizing the Day". That is banal; it needs the Latin. Prefixed, of course, with the trademark "on".
• So what is the construction? "carpentem diem" would seem to make sense. It is the logical extension of assuming that "carp -o -ere" is second (or indeed fourth) conjugation, and constructing the present participle from that root. But is the present participle the relevant part of speech? Depending on its place within the grammatical structure of the sentence, it may function as a gerund or indeed a gerundive (I have never understood what the difference is between them--and the more I quiz others [including my old friend Rodney, who must be the only surviving specimen of that wondrous species--the passionate classics master] about it, the less I understand.)
• So should I write "On 'carpentem diem'"? Or, of course, does the preposition take the dative or the ablative? It doesn't matter in practice, because the results will be the same....

However! What was this post supposed to be about? Sorry! I've forgotten.

I tried to sort out merely the title of this piece in an largely-forgotten and little practised language. At least the script was familiar.

Do you have overseas students?