〜にもかかわらず
despite, even though
Noun / Plain form + にもかかわらず (な-adj, Noun + である)
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にもかかわらず means "despite": 雨にもかかわらず、多くの人が集まった, "despite the rain, lots of people turned up".
The first half is a fact that you'd expect to prevent the second, but it didn't. It's the formal, written equivalent of のに, without のに's note of complaint, so it's also used for gratitude: 忙しいにもかかわらず、手伝ってくれてありがとう.
It follows nouns directly, and plain forms of verbs and adjectives; な-adjectives and nouns can take である.
The も is essential: without it, にかかわらず means "regardless of". At the start of a sentence, それにもかかわらず means "nevertheless".
Examples
雨にもかかわらず、多くの人が集まった。
Despite the rain, lots of people turned up.
一生懸命勉強したにもかかわらず、不合格だった。
Despite studying really hard, I failed.
注意されたにもかかわらず、彼はまた遅刻した。
Despite being warned, he was late again.
忙しいにもかかわらず、手伝ってくれてありがとう。
Thank you for helping, even though you're so busy.
休日であるにもかかわらず、会社に行った。
Even though it was a holiday, I went to work.