In my opinion, both sentences are grammatically correct but I'm not too sure how the v+ing can be used in this particular situation:
1. The use of language to establish identity was nicely presented in a recent study led by Andy Baron at Harvard University.
2. The use of language to establishing identity was nicely presented in a recent study led by Andy Baron at Harvard University.
As with the first sentence, I divided the text is this manner to interpret the sentence
[The use of language] [to establish identity] was nicely presented in a recent study led by Andy Baron at Harvard University.
As with the second sentence, I divided the words in this manner to interpret the sentence.
[The use of language] to [establishing identity] was nicely presented in a recent study led by Andy Baron at Harvard University.
How does it look to you? is the 2nd sentence grammatically wrong? if it is right, is there any significant difference in the meaning each sentences convey?