[geometry-ml:05109] Kagawa Seminar(4/7)

[yotsutani.naoto ＠ kagawa-u.ac.jp]

�何学MLの皆�

(クロスポスト失礼いたします)


直前のお知らせとなり申し�ありませんが,香川大学では,次の予定で香川セミナ�を�催いたします.

もし�味を持たれた方がいらっしゃいましたら,お��にご参加ください.


香川大学教育学部数学教室

四ッ谷直仁

―――――――――――――――――――――――

《日�》2023年4月7日 13:30-15:00

《形式》�面

《�所》香川大学教育学部8号�: 2F L-822 教室

《�演者》Grigory Solomadin (�山理科大学)

《タイトル》Finite topologies and cohomology of sheaves. (English)

《アブストラクト》

Complex-analytical or algebraic sheaves and their cohomology provide indispensable tool in complex and algebraic geometry (by Godement, Iversen, Hartshorne etc.).

This tremendous theory has a "junior brother": sheaves over finite topological spaces.

Applications of finite topological spaces (called Alexandrov topologies) have obvious limitations such as possessing only weak homotopy equivalences for CW-complexes.

However, the sheaf theory over finite posets inherits most of the tools from its "senior brother" in a very accessible form.

Mainstream algebraic topology and finite spaces are connected via combinatorics of finite spaces by theorems of McCord and Stong.

Cohomology of sheaves over finite spaces a useful tool in topological data analysis advocated by M.Curry and others.

The present talk is a brief introduction to basic theory of sheaves over posets, their cohomology and finite topologies.

Some research problems will be discussed if time permits.


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