Tuesday Seminar on Topology

[Japanese]   [Past Programs]
This is an online seminar on Zoom.

Last updated September 23, 2022
Information :@
Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai

Pre-registration is required.
Once you register, you can attend all our seminars until the end of August, 2022.

October 4, 17:00-18:00 -- Online on Zoom. Pre-registration is required.

Shuichi Harako (The University of Tokyo)

Orientable rho-Q-manifolds and their modular classes

Abstract: A rho-commutative algebra, or an almost commutative algebra, is a graded algebra whose commutativity is given by a function called a commutation factor. It is one generalization of a commutative algebra or a superalgebra. We obtain a rho-Lie algebra, or an epsilon-Lie algebra, by a similar generalization of a Lie algebra. On the other hand, we have the modular class of an orientable Q-manifold. Here, a Q-manifold is a supermanifold with an odd vector field whose Lie bracket with itself vanishes, and its orientability is described in terms of the Berezinian bundle. In this talk, we introduce the concept of a rho-manifold, which is a graded manifold whose functional algebra is a rho-commutative algebra, then we show that we can define Q-structures, Berezinian bundle, volume forms, and modular classes of a rho-manifold with some examples.

October 11, 17:00-18:00 -- Online on Zoom. Pre-registration is required.

Yasuhiko Asao (Fukuoka University)

Magnitude homology of graphs

Abstract: Magnitude is introduced by Leinster in 00fs as an ``Euler characteristic of metric spacesh. It is defined for the metric structure itself rather than the topology induced from the metric. Magnitude homology is a categorification of magnitude in a sense that ordinary homology categorifies the Euler characteristic. The speakerfs interest is in geometric meaning of this theory. In this talk, after an introduction to basic ideas, I will explain that magnitude truly extends the Euler characteristic. From this perspective, magnitude homology can be seen as one of the categorification of the Euler characteristic, and the path homology (Grigorfyan\Muranov\Lin\S-T. Yau et.al) appears as a part of another one. These structures are aggregated in a spectral sequence obtained from the classifying space of ``filtered set enriched categoriesh which includes ordinary small categories and metric spaces.