Upcoming Seminars & Events

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May 4, 2017
4:30pm - 5:30pm
TBA - Jared Weinstein
Speaker: Jared Weinstein , Boston University
Location:
Fine Hall 214
May 4, 2017
4:30pm - 5:30pm
TBA - John Pardon
Speaker: John Pardon, Princeton University
Location:
Fine Hall 314
May 10, 2017
2:30pm - 3:30pm
TBA - Joe Zhong
Speaker: Joe Zhong, Princeton University
Location:
Fine Hall 224
May 11, 2017
4:30pm - 5:30pm
TBA - Ananth Shankar
Speaker: Ananth Shankar , Harvard University
Location:
IAS Room S-101
May 18, 2017
4:30pm - 5:30pm
Potential automorphy of some non-self dual Galois representations

The IAS recently organized an Emerging Topics Working Group on " Applications to modularity of recent progress on the cohomology of Shimura varieties". Based on ideas of Calegari and Geraghty, and using recent results of Khare-Thorne and Caraiani-Scholze, the group (Allen, F.Calegari, Caraiani, Gee, Helm, Le Hung, Newton, Scholze, Thorne and myself) were able to prove modularity lifting theorems for n-dimensional Galois representations over CM (or totally real) fields without a (conjugate) self-duality hypothesis. Most notably our theorems apply in the `non-minimal' case. As applications we prove that elliptic curves over CM fields become modular after a finite base change. We also prove that cohomological (for trivial coefficients) automorphic forms on GL(2) over a CM field satisfy the Ramanujan conjecture. We are not able to reduce the Ramanujan conjecture to the Weil conjectures, rather we deduce it from the potentially automorphy of symmetric powers. 

Speaker: Richard Taylor , IAS
Location:
Fine Hall 214

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