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Channel state information (CSI) in the interference channel can be used to reduce the dimension of received interference and helps achieve the channel's maximum multiplexing gain through what is known as interference alignment (IA). Most interference alignment algorithms require knowledge of all the interfering channels to compute the alignment precoders. CSI, considered available at the receivers, can be shared with the transmitters via limited feedback. When IA is done by coding over frequency extensions in a single antenna system, the required CSI lies on the Grassmannian manifold and its structure can be exploited in feedback. Unfortunately, the number of channels to be shared grows with the square of the number of users, creating too much overhead with conventional feedback methods. This paper proposes Grassmannian differential feedback to reduce feedback overhead by exploiting both the channel's temporal correlation and Grassmannian structure. The performance of the proposed algorithm is characterized both analytically and numerically as a function of channel length, mobility, and the number of feedback bits. The main conclusions are that the proposed feedback strategy allows IA to perform well over a wide range of Doppler spreads, and to approach perfect CSI performance in slowly varying channels. Numerical results highlight the trade-off between the frequency of feedback and the accuracy of individual feedback updates.