Wiles proof of Fermat's Last Theorem is known
in number theory by another name: The Modularity Theorem. It
states that elliptic curves which are defined over the rational numbers
are attached in a precise way to modular forms. In this talk, I
will explain some of the ingredients of the Modularity Theorem and
describe a particular generalization called the Paramodular
Conjecture. I will also explain some joint work with Brooks
Roberts which proves the Paramodular Conjecture in certain special
cases.
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