Geometry and Differential Equations Seminar

Time and place: IMPAN, room 403, Wednesday, 12:15-13:45

Organisers: Bronisław Jakubczyk, Paweł Nurowski, Wojciech Kryński


Septembet 27, 2017

Christoph Harrach (University of Vienna): Poisson transforms for differential forms adapted to homogeneous parabolic geometries

ABSTRACT: We present a construction of Poisson transforms between differential forms on homogeneous parabolic geometries and differential forms on Riemannian symmetric spaces tailored to the exterior calculus. Moreover, we show how their existence and compatibility with natural differential operators can be reduced to invariant computations in finite dimensional representations of reductive Lie groups.

Septembet 20, 2017

Shin-Young Kim (Masaryk University, Brno): Geometric structures modeled on some horospherical varieties

ABSTRACT: To prove Hwang-Mok's deformation rigidity problems modeled on projective complex parabolic manifolds, we studied geometric structures arising from varieties of minimal rational tangents. To generalize these rigidity results to quasihomogeneous complex manifolds, we study a smooth projective horospherical variety of Picard number one and their geometric structures. Using Cartan geometry, we prove that a geometric structure modeled on a smooth projective horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one. In this seminar, we also briefly introduce the origin of this specific problem and horospherical varieties which are completely different from horospheres.

Septembet 13, 2017

Sean Curry (University of California, San Diego): Compact CR 3-manifolds, and obstruction flatness

ABSTRACT: We motivate and consider the problem of determining whether the vanishing of the Fefferman ambient metric obstruction implies local flatness for compact CR 3-manifolds, possibly embedded in C^2.