Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Ana Caraiani
Affiliation:

Imperial College, London
Date:

Fri, 23/11/2018 - 15:30 - 16:30 I will discuss joint work in progress with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne on potential automorphy over CM fields. I will give an overview of this work and mention some applications. I will then focus on how to prove one of our key inputs, namely local-global compatibility at $l=p$ for certain Galois representations attached to torsion classes in the cohomology of locally symmetric spaces. This relies crucially on some ingredients from representation theory in positive characteristic.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/8209