1. Period mappings: the elliptic case - and hypergeometric functions.
Javier Fresán
[Y], and [G] for the historical viewpoint (from Gauss to Riemann and Schwarz).
2. Period mappings: the case of abelian varieties with prescribed endomorphisms.
Yohan Brunebarbe
Period domains and mappings, Gauss-Manin connection, Hodge filtration. [CMP] [A, II1]
3. Moduli spaces of abelian varieties with prescribed endomorphisms.
Victoria Cantoral Farfán
Shimura varieties of PEL type, Example: Shimura curves. [CMP] [A, II1] [Cl]
4. Abelian varieties and $p$-divisible groups.
Diego Izquierdo
Serre-Tate theorem. [A, II2]
5. Dieudonné modules of $p$-divisible groups.
Ramla Abdellatif
Grothendieck-Messing theorem. [A, II3]
6. Moduli spaces of $p$-divisible groups.
Brian Lawrence
Rapoport-Zink spaces. [A, II4] [RZ]
7. $p$-adic period domains/mappings.
Salim Tayou
Relation to the Gauss-Manin connection. [A, II5, 6] [RZ]
8. $p$-adic local (sometimes global) uniformization of Shimura varieties.
Giacomo Graziani
Rapoport-Zink theorem. [A, II7] [RZ]
9. Example: $p$-adic uniformization of Shimura curves and period mappings.
Yunqing Tang
Cherednik-Drinfeld theorem, relation to the Gauss-Manin connection. [A, II 7.4, III 4.7]
10. Tempered coverings and fundamental group.
Pedro Ángel Castillejo
[A, III 2] [L]
11. Orbifolds and uniformizing differential equations (complex and $p$-adic).
Daniele Turchetti
[A, III 4]
12. (complex and $p$-adic) triangle groups.
Peter Jossen
[A, III 5, 6]
13. $p$-divisible groups over $O_C$: isotriviality.
Sergey Gorchinskiy
[SW 5.1.4]
14. $p$-divisible groups over $O_C$: classification.
Paul Ziegler
[SW 5.2.1]
Additional Talk
Rigid connections, $F$-isocrystals and integrality
Hélène Esnault
On a smooth complex projective variety, Carlos Simpson conjectures that a rigid integrable connection is motivic. This in particular implies that the monodromy is integral. We prove the integrality conjecture when the connection defines a smooth moduli point. To this aim, we prove that the mod p reduction of a rigid integrable connection has the structure of an isocrystal with Frobenius structure. We also prove that rigid integrable flat connections with vanishing $p$-curvatures are unitary. This allows one to prove new cases of Grothendieck’s $p$-curvature conjecture. Joint work with Michael Groechenig.