Tuesday Seminar on Topology

17:00 -- 18:30 Graduate School of Mathematical Sciences, The University of Tokyo
Tea: 16:30 -- 17:00 Common Room

Last updated September 15, 2017
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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)

Representations of Semisimple Lie Groups and Penrose Transform

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)

Transitional geometry

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 AfCampo and recent joint work with AfCampo and Yi Huang.

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

Shoji Yokura (Kagoshima University)

Poset-stratified spaces and some applications

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)

Generalizations of twisted Alexander invariants and quandle cocycle invariants

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.