log

January 18 (Wed.) 15:00-18:00
pre-presentation of master thesis


November 30 (Wed.) 15:00-18:00
Intermediate report for master theses


25 October (Tue) 14:00 - 15:00
Prof. Alan Huckleberry (Ruhr Univ., Bochum)

On complex geometric curvature of flag domains

Abstract:
Flag domains are complex manifolds which arise as open orbits of real Lie groups in flag manifolds of their
complexifications. They play an important role in the theory of parameter spaces of complex structures on
compact algebraic manifolds (period domains, Hodge theory, Mumford-Tate domains) and in the representation
theory of semisimple Lie groups.In the lecture we will discuss flag domains from the complex analytic viewpoint,
in particular discussing their Levi curvature. Classical results which use their intrinsic Hermitian geometry,
and which yield strong statements about the degree of positivity of the Levi form, will be outlined. Recent
results of the speaker and his co-authors which contribute to understanding the negative curvature
(pseudoconcavity) will be presented. While the results on the positive side lead to vanishing of cohomology
in high degree, results on pseudoconcavity can be applied in the low range and thereby lead to information about
the function-theoretic phenomena of these domains.


17 April (Wed) 16:30 - 17:30
Prof. Isac Heden (RIMS)

Extensions of principal additive bundles over a punctured surface.

Abstract: We study complex affine G_a-threefolds X such that the
restriction of the quotient morphism \pi\colon X\to S to \pi^{-1}(S_*)
is a principal G_a-bundle, where S_* denotes the complement of a
closed point in S. Changing the point of view, we look for affine
extensions of G_a-principal bundles over punctured surfaces, i.e
affine varieties that are obtained by adding an extra fiber to the
bundle projection over the puncture. The variety SL_2 will be of
special interest and a source of many examples.