Tea: 16:30 -- 17:00 Common Room

Information :@

Toshitake Kohno

Nariya Kawazumi

Takahiro Kitayama

Takuya Sakasai

September 26 [Joint with Lie Groups and Representation Theory Seminar] -- Room 056, 17:00 -- 18:30

Hideko Sekiguchi (The University of Tokyo)

Abstract: The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.

October 3 -- Room 056, 17:00 -- 18:30

Athanase Papadopoulos (IRMA, Université de Strasbourg)

Abstract: I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert AfCampo and recent joint work with AfCampo and Yi Huang.

October 10 -- Room 056, 17:30 -- 18:30

Shoji Yokura (Kagoshima University)

Abstract: A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).

October 17 -- Room 056, 17:00 -- 18:30

Atsushi Ishii (University of Tsukuba)

Abstract: We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an augmented Alexander pair, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro.