[geometry-ml:05457] 信州トポロジーセミナー・関西代数トポロジーセミナー(1/30)

[松下尚弘]

皆様、

このお知らせを重複して受け取られた方はご容赦ください。

信州大学理学部数学科（松本キャンパス）では、不定期に信州トポロジーセミナーを開催しています。この度、2024年1月30日に、関西代数トポロジーセミナーとの共催で対面形式のセミナーを下記の要領で予定しております。皆様のご参加をお待ちしております。

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2024年1月30日（火）14:15--15:45 **関西代数トポロジーセミナーとの共催**
題目： A theory of plots
講演者： 山口 睦（大阪公立大学）
会場： 理学部A棟4階 数理・自然情報合同研究室(A-401)
概要： The notion of plots in diffeology is introduced to define diffeological
spaces which generalize differentiable manifolds. We observe that the
notion of plots in diffeology has an easy generalization by replacing the
site (O,E) of open sets of Euclidean spaces and open embeddings by a
general Grothandieck site (C,J) and the forgetful functor U:O → Set by a
set valued functor F:C → Set. In this talk, we show that the category of
“generalized” plots is a quasi-topos, namely it is (finitely) compltete and
cocommplete, locally cartesian closed and has strong subobject classifier.
We also show that groupoids associated with epimorphisms can be defined as
in the text book “Diffeology” by P.I-Zemmour so that we can develop the
theory of fibration in the category of “generalized” plots. Moreover, we
mention the notion of F-topology which generalizes the D-topology in
diffeology.

2024年1月30日（火）16:00--17:30 **関西代数トポロジーセミナーとの共催**
題目： Tight complexes are Golod
講演者： 岸本 大祐（九州大学）
会場： 理学部A棟4階 数理・自然情報合同研究室(A-401)
概要： Tightness of a simplicial complex is a combinatorial analogue of a
tight embedding of a manifold into a Euclidean space, studied in
differential geometry. Golodness is a property of a noetherian ring,
defined in terms of the Poincare series of its Koszul homology, and
Golodness of a simplicial complex is defined by that of the Stanley-Reisner
ring. Recent results on polyhedral products suggest connection between
these two notions for manifold triangulations, and in 2023, Iriye and I
proved that they are equivalent for 3-dimensional manifold triangulations.
In this talk, I will present that tight complexes are always Golod, which
implies Golodness and tightness are equivalent for all manifold
triangulations. I will also give a quick survey on the study of Golodness
through polyhedral products.
This is a joint work with Kouyemon Iriye.

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情報の更新は下記 web ページにてお知らせいたします。

http://math.shinshu-u.ac.jp/~topology/seminar/

信州トポロジーセミナーでは、講演者を随時募集しております。
自薦・他薦などありましたら、お知らせください。
よろしくお願いします。

--

松下 尚弘（まつした・たかひろ）
信州大学理学部数学科
matsushita ＠ shinshu-u.ac.jp

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