# A Wiles-Diamond numerical criterion in higher dimensions

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Chandrashekhar Khare, UCLA
IAS - Simonyi Hall Seminar Room SH-101

In-Person and Online Talk

The patching method  has been vastly generalized; in particular Calegari-Geraghty  found a way to generalize it in principle to prove (potential) modularity of elliptic curves over imaginary quadratic fields (a situation of positive defect’’).  Their method has been made unconditional to prove  modularity lifting results  over CM fields in the ten author paper. The numerical criterion has yet to be be generalized to positive defect.