Essen Spring School towards a mod p Langlands correspondence (April 2021)

Talk notes

• Talk 1: Cohomology of Shimura curves and Gelfand-Kirillov dimension, introduction (Benjamin Schraen)
• Talk 2: The mod $p$ local Langlands correspondence for $GL_2(\mathbb Q_p)$ via $(\varphi,\Gamma)$-modules (Stefano Morra)
• Talk 3: Serre weights and diagrams for $GL_2(\mathbb Q_{p^f})$ (a survey of [Breuil-Paškūnas]) (Christophe Breuil)
• Talk 4: Functor $D$ to $(\varphi,\Gamma)$-modules and a lower bound for $D(\pi)$ (Florian Herzig)
• Talk 5: Multivariable $(\varphi,\Gamma)$-modules (Benjamin Schraen)
• Talk 6: Self-duality of the cohomology; finiteness results in the semisimple case (Yongquan Hu)
• Talk 7: Computation with multi-Hodge type deformation rings (Stefano Morra)
• Talk 8: Lattices, patching, and multiplicity one for the Iwahori (Florian Herzig)
• Talk 9: Finiteness results in the non-semisimple case (Yongquan Hu)
• Talk 10: Conjectures for $GL_n$ (Christophe Breuil)