Fred Irvin Diamond (born November 19, 1964) is a mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations.
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👉 Fred Diamond in the context of Brian Conrad
Brian Conrad (born November 20, 1970) is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University.
Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture. He proved this in 1999 with Christophe Breuil, Fred Diamond and Richard Taylor, while holding a joint postdoctoral position at Harvard University and the Institute for Advanced Study in Princeton, New Jersey.
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Fred Diamond in the context of Modularity theorem
In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem (FLT). Later, a series of papers by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, culminating in a joint paper with Christophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001. Before that, the statement was known as the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture, or the modularity conjecture for elliptic curves.
View the full Wikipedia page for Modularity theorem