■ Keizo Yamaguchi (Hokkaido U.)

                                                                                                    Abstract PDFfile Download

■ Dennis The (U. Tromso)

- Title: Exceptionally simple PDE

- Abstract: Arguably one of the most beautiful results of 19th century mathematics was the classification of complex simple Lie algebras due to Cartan and Killing.  Beyond the four classical families of matrix Lie algebras, five mysterious "exceptional simple" Lie algebras made their first appearance in this story.  In 1893, the smallest of these, G2, was first realized by Cartan and Engel as the infinitesimal symmetries of various geometric structures.  In this talk, I will review this story and discuss how it was recently generalized in a remarkably uniform manner to obtain analogous explicit geometric realisations for (almost) any complex simple Lie algebra. 

■ Katharina Neusser (Charles U.)

- Title: C-projective Equivalence in Kähler Geometry

- Abstract: While a projective structure on a manifold is given by a class of affine connections that have the same (unparametrised) geodesics, a c-projective structure on a complex manifold is given by a class of affine complex connections that have the same ``J-planar'' curves. In this talk we will be mainly concerned with c-projective structures induced by K"ahler metrics (via their Levi-Civita connections) and present some work on the geometric and topological consequences of the existence of at least two c-projectively equivalent K"ahler metrics. An application of these considerations is a proof of the Yano--Obata conjecture for complete Kähler manifolds---a metric c-projective analogue of the conformal Lichnerowicz conjecture. This talk is based on joint work with Calderbank--Eastwood--Matveev, and with Matveev.

■ Qifeng Li (KIAS)

- Title: An existence theorem for Cartan connections

- Abstract: In this talk we will give an existence theorem for Cartan connections on manifolds equipped with geometric system modeled after G/H, where G is a complex (possibly non-reductive) linear algebraic group, and H is a (possibly non-parabolic) subgroup. In contrast, we require vanishing of global sections over M of some vector bundles. We will apply our theorem to study local nature of some algebraic varieties from the variety of lines on them. This is a joint work with Jun-Muk Hwang.