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[信州大学]
[理学部]
[数学科]
390-8621 長野県松本市旭3-1-1 |
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管理者：松下 尚弘 ---matsushita(at)shinshu-u.ac.jp |
[ 講演予定 ] [ これまでの講演 ] [ Algebraic Toplogy: A guide to literature ] [ English ]
| 題目： | On nonstandard and asymptotic extensions of smooth maps between diffeological spaces |
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| 講演者： | 島川 和久（岡山大学） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 題目： | Linking-number-type functions and application to Authentication technology |
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| 講演者： | Kamolphat Intawong（茨城工業高等専門学校） |
| 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 Gauss linking number is represented by the simplest Gauss diagram.
We consider inserting one arrow to the Gauss diagram, and have new invariants called multiple linking number.
Then, we apply these functions to information technology.
In the information society, it is essential to continue developing information security technology. Recently, various approaches, such as quizzes, have been taken. In this study, we apply a specific characteristic of functions that we introduced to create quizzes for authentication. |
| 題目： | Integrating curvature and a quantization of Arnold strangeness invariant |
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| 講演者： | 伊藤 昇（茨城工業高等専門学校） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 概要： | Arnold basic invariants consist of three classical invariants of generic plane curves. Two of them have been successfully quantized by Viro (1996) and Lanzat-Polyak (2013). However, the quantization of the last one, the Arnold strangeness invariant "St", remained unrealized. In this talk, we express a quantization of the Arnold strangeness by integrating curvatures multiplied by densities. In this quantization, the first term of the Taylor expansion at q=1 corresponds to the rotation number, the second term to the Arnold strangeness invariant, the higher terms to the Tabachnikov invariants. |
| 題目： | sclと粗い群 |
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| 講演者： | 見村 万佐人（東北大学） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 概要： | 川﨑盛通（北大）、木村満晃（京都大）、松下尚弘（信州大）、丸山修平（金沢大）各氏との共同研究です。 安定交換子長（scl：stable commutator length）はその値の数論的な性質（例えば、有理数であるかなど）や取り得る非零値に正の下界があるか（ギャップ定理）など、精密な値についての深い結果群が知られています。 他方、本研究では、群の間の "距離" を scl で定める、という形での "距離空間" の性質を考えます。 この "距離" は一般に三角不等式を満たさないという致命的な欠陥があるのですが、小スケールの構造を破壊した粗い幾何学（coarse geometry）の観点では距離空間と思うことができます。 このような、「scl の粗い幾何」という新鮮な見方での研究成果をお話しします。実はより細かく、群に scl から定まる（粗い幾何の意味での）距離を入れた空間は粗い幾何の圏での群対象と見ることができます。 この概念は「粗い群（coarse group）」と呼ばれ、Leitner と Vigolo による 2024 年出版予定のモノグラフで理論が大きく進んでいます。 scl の粗い群的な視点での一般論、および、応用例としてトレリ群の元でかつ擬アノソフな写像類による写像トーラスの基本群の場合についてお話しします。 |
| 題目： | A theory of plots |
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| 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. |
| 題目： | Tight complexes are Golod |
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| 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. |