There "is" / "are" a lot of...

- There is a lot of corn in the store.
- There are a lot of corn in the store.
The word "corn" here is a singular noun, so the first is correct and the second is wrong, isn't it?

- There is a lot of people in the store.
- There are a lot of people in the store.
The word "people" here is a plural noun, so the first is wrong and the second is correct, isn't it?

Similar thread: http://www.eslhq.com/forums/esl-forums/english-questions/subject-verb-agreement-2206/