Yes, they are both gramatically correct, and there's no difference in meaning. In examples where a gerund-participial clause is complement to a preposition like "at", then it's a free choice between using a genitive case or accusative case subject. The only difference is one of formality, with the genitive "my" being a tad more formal than the non-genitive "me"; that's all.
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BillJIn examples where a gerund-participial clause is complement to a preposition like "at"It also applies to verb complements.
AlpheccaStarsIt also applies to verb complements.I wonder, though, what the consensus is regarding its use as a subject.