## Michaelmas 2017: Drinfeld Upper Half Plane

The goal is to understand the Drinfeld upper half plane, following a paper by Boutot-Carayol.
An English translation of the paper can be found [here]( http://www-personal.umich.edu/~francc/files/bctranslation.pdf).

### Schedule

1. Thursday 19/10/2017, 4pm, MR13: Motivation (Zhiyou); [notes](https://www.mathi.uni-heidelberg.de/~mleonhardt/talk1_Zhiyou.pdf)
2. Thursday 26/10/2017, 3pm, MR4: The Bruhat-Tits tree of $PGL_2(K)$ (Beth)
3. Thursday 02/11/2017, 4pm, MR13: Formal and functorial versions of the upper half plane (Ben)
4. Thursday 09/11/2017, 3pm, MR13: Formal $\mathcal{O}$-modules and statement of the 'Basic Theorem' (Christos); [notes](https://www.mathi.uni-heidelberg.de/~mleonhardt/talk4_christos-notes.pdf)
5. Thursday 16/11/2017, 4pm, MR13: Sketch of proof of the 'Basic Theorem' (Axel); [notes](https://www.mathi.uni-heidelberg.de/~mleonhardt/talk5_axel.pdf)
6. Thursday 23/11/2017, 3pm, MR13: Quaternion algebras and Shimura curves (Marius)
7. Monday 04/12/2017, 3pm, MR13: An application of $p$-adic uniformization to level-lowering (Jack)
8. Wednesday 06/12/2017, 3pm, MR13: Cerednik-Drinfeld Theorem - $p$-adic uniformization (Zhiyou)