Matthew James Emerton (born 9 November 1971) is an Australian mathematician who is a professor of mathematics at the University of Chicago.
[1] He earned his PhD in 1998 from Harvard University (where he studied under Barry Mazur and his PhD thesis was titled "2-Adic Modular Forms of Minimal Slope" [2]) and a BS (honors) from the University of Melbourne.
[4] Emerton introduced the notion of completed cohomology, which has proved to be a useful tool in the study of the p-adic theory of automorphic forms.
[5] Using this theory, together with the work of Colmez on the p-adic Langlands program, he posted a preprint in 2011 proving many cases of the Fontaine--Mazur conjecture.
[5] Emerton was a Sloan fellow in 1997[4] and was an invited speaker at the 2014 ICM in Seoul where he gave a talk entitled "Completed cohomology and the p-adic Langlands program".