Hello, Jump4Fun, and welcome to the Grammar Exchange.
@Jump4Fun posted:I'm curious about the grammatical construction of this sentence: I am glad you are here. It appears to contain 2 independent clauses, which doesn't seem right (no conjunction) . Possibly "that" is understood which would make the second clause dependent, but again, that really doesn't seem right either.
The conjunction "that" is omitted, so you do have a main clause, I am glad, and a subordinate one, you are here. "That" introduces an adverbial clause of reason.