|
[
Department of Mathematics] [Shinshu University] Matsumoto, 390-8621 |
|
Editor of this web site; Takahiro Matsushita ---matsushita(at)shinshu-u.ac.jp |
[ Schedule ] [ Archives ] [ Algebraic Toplogy: A guide to literature ] [ Japanese ]
| Title: | On nonstandard and asymptotic extensions of smooth maps between diffeological spaces |
|---|---|
| Speaker: | Kazuhisa Shimakawa (Okayama University) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Title: | Linking-number-type functions and application to Authentication technology |
|---|---|
| Speaker: | Kamolphat Intawong (National Institute of Technology, Ibaraki College) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: |
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. |
| Title: | Integrating curvature and a quantization of Arnold strangeness invariant |
|---|---|
| Speaker: | Noboru Ito (National Institute of Technology, Ibaraki College) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: | 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. |
| Title: | scl and coarse groups |
|---|---|
| Speaker: | Masato Mimura (Tohoku University) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: | This is a joint work with Morimichi Kawasaki (Hokkaido), Mitsuaki Kimura (Kyoto), Shuhei Maruyama (Kanazawa) and Takahiro Matsushita (Shinshu). We study scl (stable commutator length) from coarse group theoretic viewpoints; the concept of coarse groups is developed in the recent monograph by Leitner and Vigolo. |
| Title: | A theory of plots |
|---|---|
| Speaker: | Atsushi Yamaguchi (Osaka Metropolitan University) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: | 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. |
| Title: | Tight complexes are Golod |
|---|---|
| Speaker: | Daisuke Kishimoto (Kyushu University) |
| Room: | A-401, Faculty of Science, Shinshu University |
| Abstract: |
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. |