"There is nothing" is correct.
These words are conjugated in the third person singular: nothing, nobody, no one, something, somebody, someone, everything, everybody, everyone.
In the case of the last group, it's sounds a bit confusing because everything, everybody, and everyone refer to a group. Here's another way of looking at it: "Every book HAS a title. Again, we are referring to all books, but we conjugate the verb in the third person singular.