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Following the tradition of recent summer schools organized in the framework of the cooperation Berlin-Holland
a joint summer school will take place in the Netherlands in 2017. Date: August 27th to September 1st, 2017
Location: Grand Hotel Opduin, Texel Island, The Netherlands
Main Speakers:
Ana Caraiani (HCM Bonn)
Galois representations and torsion classes
(show abstract [here])
Galois representations and torsion classes
(hide abstract [here])
The goal of this mini-course is to describe some recent progress in computing the cohomology of unitary Shimura with torsion coefficients as well as applications of these results to Galois representations for torsion classes. I will focus on the underlying geometry, and discuss perfectoid Shimura varieties, the Hodge-Tate period morphism and its interaction with the Newton stratification. The mini-course will rely primarily on joint work with Peter Scholze.
Olivier Debarre (U Paris Diderot)
Hyperkähler Manifolds
(show abstract [here])
Hyperkähler Manifolds
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Hyperkähler manifolds are higher-dimensional analogues of K3 surfaces. We will review classical results on (complex) K3 surfaces and discuss recent results on hyperkähler manifolds, mostly consequences of the Torelli theorem (results of Verbitsky and Markman) and of the determination of their ample cone in some cases (results of Bayer and Macrì). I will concentrate on the projective case and discuss projective embeddings.
Steven Sam (Univ. of Wisconsin, Madison)
Representation stability
(show abstract [here])
Representation stability
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Representation stability describes a phenomenon in which a sequence of representations of groups stabilizes in a suitable sense. This can be understood in terms of representations of categories whose automorphism groups are the groups in question and the other morphisms describe transition maps between the representations. I plan to discuss a few examples of such categories: FI, the category of finite sets and injective functions, and FS^op, the opposite category of finite sets and surjective functions, and some of their applications in topology and algebraic geometry.
Olivier Wittenberg (ENS, Paris)
Cohomology and algebraic cycles on real varieties
(show abstract [here])
Cohomology and algebraic cycles on real varieties
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If -1 can be written as a sum of squares in the function field of a real
threefold, can it be written as a sum of 7 squares? Do real quartic
threefolds contain rational curves? These two questions are open.
In these lectures, taking such questions as a starting point, I will give
an introduction to some topics in the study of algebraic cycles on real
algebraic varieties, with an emphasis on connections with Hodge theory.
Organizers:
Bas Edixhoven (U Leiden)
Gavril Farkas (HU Berlin)
Gerard van der Geer (U Amsterdam)
Jürg Kramer (HU Berlin)
Lenny Taelman (U Amsterdam)
Registration is closed
Schedule: [here]
Participants: [here]
Travel information:
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