event
Vendredi 22 avril 2016
Vendredi 22 avril 2016
place
IRMA
IRMA
Le septième Karlsruhe-Heidelberg-Strasbourg "Geometry Day" aura lieu à Strasbourg le 22 avril 2016.
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Vendredi 22 avril 2016
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10:30
Accueil des participants
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11:00
Nicolaus Treib, Heidelberg
Schottky representations in symplectic groups
Classical hyperbolic Schottky groups are obtained by dividing a set of disjoint half spaces into pairs and choosing one generator for each pair. We mimic this construction to obtain free subgroups of Sp(2n,R) acting properly discontinuously on an open dense domain in RP^{2n-1}: First, we describe how a natural involution associated to a pair of transverse Lagrangians gives rise to a separating hypersurface in projective space. Choosing pairs of Lagrangians in positive configuration then allows to obtain disjoint half spaces that we can pair. We also study maximality of symplectic Schottky representations and apply the construction to count connected components of maximal representations of surfaces with boundary. This is joint work with JP Burelle. -
12:00
Repas
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14:00
Petra Schwer, KIT
Folding galleries in Euclidean buildings
We will discuss a Kostant type convexity theorem for Euclidean buildings, which is a statement on nonemptiness of intersections of certain double cosets in the underlying algebraic group. For the proof the statement is translated to the existence of certain folded galleries in Euclidean Coxeter complexes. Affine Deligne-Lusztig varieties can be described by similar intersections of double cosets and we will show that the question of nonemptiness and dimensions of these varieties can also be studied using folded galleries. -
15:00
Pause
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15:30
Bruno Klingler, Université Paris-Diderot
Chern's conjecture for special affine manifolds
An affine manifold X is a manifold admitting an atlas of charts with value in an affine space V with locally constant change of coordinates in the affine group Aff(V) of V. Equivalently, it is a manifold admitting a flat torsion free connection on its tangent bundle. Around 1955 Chern asked if there is any topological obstruction to the existence of an affine structure on a compact manifold X. He conjectured that the Euler characteristic e(TX) of any compact affine manifold has to vanish. I will discuss this conjecture and a proof when X is special affine (i.e. X is affine and moreover admits a parallel volume form).