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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： | Index theory for quarter-plane Toeplitz operators via extended symbols |
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| 講演者： | 林 晋（青山学院大学） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 概要： | 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 Duducava’s idea to use Gohberg-Krein’s 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. |
| 題目： | Torsion in classifying spaces of gauge groups |
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| 講演者： | 亀子 正喜（芝浦工業大学） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 概要： | Tsukuda showed that the integral homology of the classifying space of the gauge group of the nontrivial SO(3)-bundle over the 2-dimensional sphere has no torsion. SO(3) is isomorphic to the projective unitary group PU(2). I will generalize Tsukuda's result on the SO(3)-bundle to PU(n)-bundles. This talk is based on my paper with the same title, published online on April 1, 2024, in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. |
| 題目： | TBA |
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| 講演者： | 吉岡 玲音（東京大学） |
| 会場： | 理学部A棟4階 数理・自然情報合同研究室(A-401) |
| 概要： | TBA |