トポロジー火曜セミナー

開催情報 火曜日　17:00～18:30　数理科学研究科棟(駒場) 056号室 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也 http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html Tea: 16:30 - 17:00 コモンルーム

2022年10月11日(火)

17:00-18:00   オンライン開催

Magnitude homology of graphs (JAPANESE)
[ 講演概要 ]
Magnitude is introduced by Leinster in 00’s as an Euler characteristic of metric spaces”. 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’s 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’yan—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" which includes ordinary small categories and metric spaces.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html