The aim of the workshop is to understand the recent work of Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, and Benjamin Schraen in 2102.06188, 2009.03127 and by Yongquan Hu and Haoran Wang in 2009.09640 concerning the representations appearing in the Hecke eigenspaces of mod $p$ completed cohomology.

Format: The workshop will be held on Zoom. We plan to have two 90 minutes talks a day: one in the morning and one in the afternoon. The notes and recordings will be posted online. Please register for the school if you wish to attend Zoom talks live and take part in virtual social events.


All times are German times (CEST, Central European Summer Time).

Monday, April 26
10:30am - 12:00pm Benjamin Schraen Cohomology of Shimura curves and Gelfand-Kirillov dimension, introduction
3:30pm - 5:00pm Stefano Morra The mod $p$ local Langlands correspondence for $GL_2(\mathbb Q_p)$ via $(\varphi,\Gamma)$-modules
Tuesday, April 27
10:30am - 12:00pm Christophe Breuil Serre weights and diagrams for $GL_2(\mathbb Q_{p^f})$ (a survey of [Breuil-Paškūnas])
3:30pm - 5:00pm Florian Herzig Functor $D$ to $(\varphi,\Gamma)$-modules and a lower bound for $D(\pi)$
Wednesday, April 28
10:30am - 12:00pm Benjamin Schraen Multivariable $(\varphi,\Gamma)$-modules
3:30pm - 5:00pm Yongquan Hu Self-duality of the cohomology; finiteness results in the semisimple case
5:15pm - Question and Answer session
Thursday, April 29
10:30am - 12:00pm Stefano Morra Computation with multi-Hodge type deformation rings
3:30pm - 5:00pm Florian Herzig Lattices, patching, and multiplicity one for the Iwahori
Friday, April 30
10:30am - 12:00pm Yongquan Hu Finiteness results in the non-semisimple case
3:30pm - 5:00pm Christophe Breuil Conjectures for $GL_n$
5:15pm - Question and Answer session


Christophe Breuil
Florian Herzig
Yongquan Hu
Stefano Morra
Benjamin Schraen