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17:00 -- 18:00 Zoom でのオンライン開催

Last updated November 29, 2021
世話係 
河澄 響矢
北山 貴裕
逆井 卓也


今年度の冬学期もまたオンライン形式にて当セミナーを開催します.
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12 月 21 日のセミナーは Lie 群論・表現論セミナーと合同で行います.
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10月5日 -- Zoom でのオンライン開催, 17:00 -- 18:00

合田 洋 (東京農工大学)

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Abstract: We discuss a relationship between the chirality of knots and higher dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic 3-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic 3-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations. (This is a joint work with Takayuki Morifuji.)


10月12日 -- Zoom でのオンライン開催, 17:00 -- 18:00

飯田 暢生 (東京大学大学院数理科学研究科)

Seiberg-Witten Floer homotopy and contact structures

Abstract: Seiberg-Witten theory has been an efficient tool to study 4-dimensional symplectic and 3-dimensional contact geometry. In this talk, we introduce new homotopical invariants related to these structures using Seiberg-Witten theory and explain their properties and applications. These invariants have two main origins:
1. Kronheimer-Mrowka's invariant for 4-manifold with contact boundary, whose construction is based on Seiberg-Witten equation on 4-manifolds with conical end.
2. Bauer-Furuta and Manolescu's homotopical method called finite dimensional approximation in Seiberg-Witten theory.
This talk includes joint works with Masaki Taniguchi(RIKEN) and Anubhav Mukherjee(Georgia tech).


10月19日 -- Zoom でのオンライン開催, 17:00 -- 18:00

四之宮 佳彦 (静岡大学)

Period matrices of some hyperelliptic Riemann surfaces

Abstract: In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form w2=z(z2-1)(z2-a12)(z2-a22) … (z2-ag-12) (1< a1 < a2 < … < ag-1). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.


10月26日 -- Zoom でのオンライン開催, 17:00 -- 18:00

粕谷 直彦 (北海道大学)

On the strongly pseudoconcave boundary of a compact complex surface

Abstract: On the strongly pseudoconvex (resp. pseudoconcave) boundary of a complex surface, the complextangency defines a positive (resp. negative) contact structure. Bogomolov and De Oliveira proved that the boundary contact structure of a strongly pseudoconvex surface is Stein fillable. Therefore, for a closed contact 3-manifold, Stein fillability and holomorphic fillability are equivalent. Then what about the boundary of a strongly pseudoconcave surface? We prove that any closed negative contact 3-manifold can be realized as the boundary of a strongly pseudoconcave surface. The proof is done by establishing holomorphic handle attaching method to the strongly pseudoconcave boundary of a complex surface, based on Eliashberg's handlebody construction of Stein manifolds. This is a joint work with Daniele Zuddas (University of Trieste).


11月2日 -- Zoom でのオンライン開催, 17:00 -- 18:00

野坂 武史 (東京工業大学)

メタ冪零的むすび目不変量と、自由冪零群の自己同型群

Abstract: ファイバー結び目やhomology cylinderというクラスは興味深い幾何・代数的な議論が幾つか展開されてきた。 逆に本研究では、ホモロジー3-球面内の任意の結び目をそれらのクラスの様に扱えるように、 結び目群のメタ冪零的 p-局所化を考察する。 そのモノドロミーは自由冪零群のシンプレクティック自己同型群の元と見れ、 特にその外部自己同型群の共役類からの写像は結び目の不変量を与える。 その際にジョンソン準同型の研究が扱える。本講演ではそのモノドロミーの構成と、得られた不変量の研究法を幾つか紹介する。 また最近得られた、Fox-ペアリングの視点から考察と結果も紹介する。


11月9日 -- Zoom でのオンライン開催, 17:00 -- 18:00

丸山 修平 (名古屋大学)

The spaces of non-descendible quasimorphisms and bounded characteristic classes

Abstract: A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.


11月16日 -- Zoom でのオンライン開催, 17:00 -- 18:00

湯淺 亘 (京都大学数理解析研究所)

Skein and cluster algebras of marked surfaces without punctures for sl(3)

Abstract: We consider a skein algebra consisting of sl(3)-webs with the boundary skein relations for a marked surface without punctures. We construct a quantum cluster algebra coming from the moduli space of decorated SL(3)-local systems of the surface inside the skew-field of fractions of the skein algebra. In this talk, we introduce the sticking trick and the cutting trick for sl(3)-webs. The sticking trick expands the boundary-localized skein algebra into the cluster algebra. The cutting trick gives Laurent expressions of "elevation-preserving" webs with positive coefficients in certain clusters. We can also apply these tricks in the case of sp(4). This talk is based on joint works with Tsukasa Ishibashi.


11月30日 -- Zoom でのオンライン開催, 17:00 -- 18:00

佐藤 正寿 (東京電機大学)

A non-commutative Reidemeister-Turaev torsion of homology cylinders

Abstract: The Reidemeister-Turaev torsion of homology cylinders takes values in the integral group ring of the first homology of a surface. We lift it to a torsion valued in the K1-group of the completed rational group ring of the fundamental group of the surface. We show that it induces a finite type invariant of homology cylinders, and describe the induced map on the graded quotient of the Y-filtration of homology cylinders via the 1-loop part of the LMO functor and the Enomoto-Satoh trace. This talk is based on joint work with Yuta Nozaki and Masaaki Suzuki.


12月7日 -- Zoom でのオンライン開催, 17:00 -- 18:00

佐野 岳人 (東京大学大学院数理科学研究科)

Bar-Natan ホモトピー型の構成

Abstract: 2000年に Khovanov は Jones 多項式の圏論化として Khovanov ホモロジー $H_{Kh}$ を構成した. 2014 年に Lipshitz-Sarkar は Khovanov ホモロジーの空間的実現として Khovanov ホモトピー型 $\mathcal{X}_{Kh}$ を構成した. すなわち $\mathcal{X}_{Kh}$ は空間(有限 CW スペクトラム)で,その被約コホモロジー群が Khovanov ホモロジーを復元するものである. Khovanov ホモロジーには Lee ホモロジー,Bar-Natan ホモロジーなどの変種があり, Rasmussen による $s$-不変量など重要な不変量を取り出すこともできる. これらの変種に対してホモトピー型が構成できるかどうかは2020年まで未解決であった. 講演者は 2021年 の論文で,変種の一つである Bar-Natan ホモロジー $H_{BN}$ に対して,その空間的実現である Bar-Natan ホモトピー型 $\mathcal{X}_{BN}$ を構成し,その安定ホモトピー型を決定した. $\mathcal{X}_{BN}$ の構成は $\mathcal{X}_{Kh}$ と同様に Cohen-Jones-Segal が提案したフロー圏による構成法を用いる. 安定ホモトピー型の決定は Lobb らによる「フロー圏における Morse 変形」の手法を用いる.Bar-Natan ホモトピー型 を用いた $s$-不変量の空間的精密化は今後の課題である.

https://arxiv.org/abs/2102.07529


12月21日 [Lie群論・表現論セミナーと合同] -- Zoom でのオンライン開催, 17:30 -- 18:30

島倉 裕樹 (東北大学)

Classification of holomorphic vertex operator algebras of central charge 24

Abstract: Holomorphic vertex operator algebras are imporant in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic. One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras. I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.