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17:00 -- 18:00 Zoom でのオンライン開催

Last updated September 23, 2022
河澄 響矢
北山 貴裕
逆井 卓也

2022 年度の冬学期もまたオンライン形式にて当セミナーを開催します.
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一度登録を行えば 2023年 3 月末までは再登録の必要はありませんが, トラブルが生じた場合は再登録をお願いする可能性があります.
Zoom ミーティングの開始は 16:45 頃となります. それまでは「待機室」にてお待ち下さい.

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10月4日 -- Zoom でのオンライン開催, 17:00 -- 18:00

原子 秀一 (東京大学大学院数理科学研究科)

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.

10月11日 -- Zoom でのオンライン開催, 17:00 -- 18:00

浅尾 泰彦 (福岡大学)

Magnitude homology of graphs

Abstract: 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.