De Jack Thorne
Let K be an imaginary quadratic field. Conjecturally, one should be able to associate to any cusp form on GL_n(A_K) which is cohomological (for the trivial coefficient system) a Galois representation. This can be achieved using our understanding of the classification of automorphic representations of the quasi- split unitary group U(n, n), which relies upon the stabilization of the twisted trace formula for GL_n. A detailed understanding of the local properties of these Galois representations opens up the possibility of proving automorphy lifting theorems. I will describe work in progress of a 10 author collaboration that proves such theorems, using as a starting point very important vanishing theorems for the cohomology of non-compact Shimura varieties which are work in progress of Caraiani--Scholze. A particular consequence is the Ramanujan conjecture for cohomological cusp forms in the case n = 2. (The 10 authors are Allen, F. Calegari, Caraiani, Gee, Helm, Le Hung, J. Newton, Scholze, Taylor, and myself.)
De Ramla Abdellatif
De Vincent Sécherre
De Bertrand Lemaire
De Marko Tadic
De Anne Marie Aubert
De Raphaël Beuzart Plessis
De Wen-Wei Li
De Joël Bellaïche
De Jack Thorne
De Juan Camilo Arosemena Serrato
De Amine Marrakchi
De Shirly Geffen
De Francesca Arici
