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390-8621 ’·–쌧¼–{Žsˆ®3-1-1
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---matsushita(at)shinshu-u.ac.jp
Shinshu Topology Seminar

[ u‰‰—\’è ] [ ‚±‚ê‚Ü‚Å‚Ìu‰‰ ] [ Algebraic Toplogy: A guide to literature ] [ English ]


u‰‰—\’è

2024”N4ŒŽ24“úi…j16:30--17:30
‘è–ÚF Index theory for quarter-plane Toeplitz operators via extended symbols
u‰‰ŽÒF —Ñ WiÂŽRŠw‰@‘åŠwj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF Index theory for Toeplitz operators on a discrete quarter-plane has been investigated by Simonenko, Douglas-Howe, Park, and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we consider such operators of two-variable rational matrix function symbols and revisit Duducavafs idea to use Gohberg-Kreinfs theory for factorizations of matrix-valued functions from a geometric viewpoint. We see that, through matrix factorizations and analytic continuations, the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere. By using K-theory, we show that their Fredholm indices coincide with the three-dimensional winding number of extended symbols.

2023”N“x‚Ìu‰‰

2023”N11ŒŽ22“úi…j16:30--18:00
‘è–ÚF Linking-number-type functions and application to Authentication technology
u‰‰ŽÒF Kamolphat IntawongiˆïéH‹Æ‚“™ê–åŠwZj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF 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.

2023”N11ŒŽ24“úi‹àj16:30--18:00
‘è–ÚF Integrating curvature and a quantization of Arnold strangeness invariant
u‰‰ŽÒF ˆÉ“¡ ¸iˆïéH‹Æ‚“™ê–åŠwZj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF 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.
2024”N1ŒŽ17“úi…j16:30--18:00
‘è–ÚF scl‚Æ‘e‚¢ŒQ
u‰‰ŽÒF Œ©‘º –œ²li“Œ–k‘åŠwj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF ìú±·’Êi–k‘åjA–Ø‘º–žWi‹ž“s‘åjA¼‰º®OiMB‘åjAŠÛŽRC•½i‹à‘ò‘åjŠeŽ‚Æ‚Ì‹¤“¯Œ¤‹†‚Å‚·B ˆÀ’èŒðŠ·Žq’·isclFstable commutator lengthj‚Í‚»‚Ì’l‚Ì”˜_“I‚È«Ž¿i—Ⴆ‚ÎA—L—”‚Å‚ ‚é‚©‚È‚Çj‚âŽæ‚蓾‚é”ñ—ë’l‚ɳ‚̉ºŠE‚ª‚ ‚é‚©iƒMƒƒƒbƒv’è—j‚È‚ÇA¸–§‚È’l‚ɂ‚¢‚Ä‚Ì[‚¢Œ‹‰ÊŒQ‚ª’m‚ç‚ê‚Ä‚¢‚Ü‚·B ‘¼•ûA–{Œ¤‹†‚Å‚ÍAŒQ‚ÌŠÔ‚Ì "‹——£" ‚ð scl ‚Å’è‚ß‚éA‚Æ‚¢‚¤Œ`‚Å‚Ì "‹——£‹óŠÔ" ‚Ì«Ž¿‚ðl‚¦‚Ü‚·B ‚±‚Ì "‹——£" ‚͈ê”Ê‚ÉŽOŠp•s“™Ž®‚ð–ž‚½‚³‚È‚¢‚Æ‚¢‚¤’v–½“I‚ÈŒ‡Š×‚ª‚ ‚é‚Ì‚Å‚·‚ªA¬ƒXƒP[ƒ‹‚Ì\‘¢‚ð”j‰ó‚µ‚½‘e‚¢Šô‰½Šwicoarse geometryj‚ÌŠÏ“_‚Å‚Í‹——£‹óŠÔ‚ÆŽv‚¤‚±‚Æ‚ª‚Å‚«‚Ü‚·B ‚±‚̂悤‚ÈAuscl ‚Ì‘e‚¢Šô‰½v‚Æ‚¢‚¤V‘N‚ÈŒ©•û‚Å‚ÌŒ¤‹†¬‰Ê‚ð‚¨˜b‚µ‚µ‚Ü‚·BŽÀ‚Í‚æ‚èׂ©‚­AŒQ‚É scl ‚©‚ç’è‚Ü‚éi‘e‚¢Šô‰½‚̈Ӗ¡‚Å‚Ìj‹——£‚ð“ü‚ꂽ‹óŠÔ‚Í‘e‚¢Šô‰½‚ÌŒ—‚Å‚ÌŒQ‘ÎÛ‚ÆŒ©‚邱‚Æ‚ª‚Å‚«‚Ü‚·B ‚±‚ÌŠT”O‚Íu‘e‚¢ŒQicoarse groupjv‚ƌĂ΂êALeitner ‚Æ Vigolo ‚É‚æ‚é 2024 ”No”Å—\’è‚̃‚ƒmƒOƒ‰ƒt‚Å—˜_‚ª‘å‚«‚­i‚ñ‚Å‚¢‚Ü‚·B scl ‚Ì‘e‚¢ŒQ“I‚ÈŽ‹“_‚ł̈ê”ʘ_A‚¨‚æ‚ÑA‰ž—p—á‚Æ‚µ‚ăgƒŒƒŠŒQ‚ÌŒ³‚Å‚©‚‹[ƒAƒmƒ\ƒt‚ÈŽÊ‘œ—Þ‚É‚æ‚éŽÊ‘œƒg[ƒ‰ƒX‚ÌŠî–{ŒQ‚Ìꇂɂ‚¢‚Ä‚¨˜b‚µ‚µ‚Ü‚·B
2024”N1ŒŽ30“úi‰Îj14:15--15:45 **ŠÖ¼‘㔃gƒ|ƒƒW[ƒZƒ~ƒi[‚Æ‚Ì‹¤Ã**
‘è–ÚF A theory of plots
u‰‰ŽÒF ŽRŒû –ri‘åãŒö—§‘åŠwj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF 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 ggeneralizedh 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 gDiffeologyh by P.I-Zemmour so that we can develop the theory of fibration in the category of ggeneralizedh plots. Moreover, we mention the notion of F-topology which generalizes the D-topology in diffeology.
2024”N1ŒŽ30“úi‰Îj16:00--17:30 **ŠÖ¼‘㔃gƒ|ƒƒW[ƒZƒ~ƒi[‚Æ‚Ì‹¤Ã**
‘è–ÚF Tight complexes are Golod
u‰‰ŽÒF ŠÝ–{ ‘å—Si‹ãB‘åŠwj
‰ïêF —Šw•”A“4ŠK ”—EŽ©‘Rî•ñ‡“¯Œ¤‹†Žº(A-401)
ŠT—vF 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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