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トポロジー火曜セミナー
過去の記録 ～07/26｜次回の予定｜今後の予定 07/27～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
過去の記録
2023年11月07日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Florent Schaffhauser 氏 (Heidelberg University)
Hodge numbers of moduli spaces of principal bundles on curves (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Florent Schaffhauser 氏 (Heidelberg University)
Hodge numbers of moduli spaces of principal bundles on curves (ENGLISH)
[ 講演概要 ]
The Poincaré series of moduli stacks of semistable G-bundles on curves has been computed by Laumon and Rapoport. In this joint work with Melissa Liu, we show that the Hodge-Poincaré series of these moduli stacks can be computed in a similar way. As an application, we obtain a new proof of a joint result of the speaker with Erwan Brugallé, on the maximality on moduli spaces of vector bundles over real algebraic curves.
[ 参考URL ]The Poincaré series of moduli stacks of semistable G-bundles on curves has been computed by Laumon and Rapoport. In this joint work with Melissa Liu, we show that the Hodge-Poincaré series of these moduli stacks can be computed in a similar way. As an application, we obtain a new proof of a joint result of the speaker with Erwan Brugallé, on the maximality on moduli spaces of vector bundles over real algebraic curves.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年10月31日(火)
17:30-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
千吉良 直紀 氏 (熊本大学)
原田予想IIについて (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
千吉良 直紀 氏 (熊本大学)
原田予想IIについて (JAPANESE)
[ 講演概要 ]
有限群の指標表は非常に多くの情報を含んでいる。本講演では、原田耕一郎氏による既約指標の次数の積と共役類の元の個数の積に関する予想（原田予想II）についてこれまでの概要と最近の進展について講演する。
[ 参考URL ]有限群の指標表は非常に多くの情報を含んでいる。本講演では、原田耕一郎氏による既約指標の次数の積と共役類の元の個数の積に関する予想（原田予想II）についてこれまでの概要と最近の進展について講演する。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年10月24日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
林 晋 氏 (青山学院大学)
Index theory for quarter-plane Toeplitz operators via extended symbols (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
林 晋 氏 (青山学院大学)
Index theory for quarter-plane Toeplitz operators via extended symbols (JAPANESE)
[ 講演概要 ]
We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.
[ 参考URL ]We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年10月17日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
狩野 隼輔 氏 (東北大学 数理科学共創社会センター)
Train track combinatorics and cluster algebras (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
狩野 隼輔 氏 (東北大学 数理科学共創社会センター)
Train track combinatorics and cluster algebras (JAPANESE)
[ 講演概要 ]
The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.
[ 参考URL ]The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年10月10日(火)
17:30-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
見村 万佐人 氏 (東北大学)
不変擬準同型と scl の粗い幾何 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
見村 万佐人 氏 (東北大学)
不変擬準同型と scl の粗い幾何 (JAPANESE)
[ 講演概要 ]
10/9〜13 の集中講義では Green--Tao の定理とその数体への一般化について話しますが、本講演の内容はそれとは完全に独立しています。川崎盛通氏（北海道大学）、木村満晃氏（京都大学）、松下尚弘氏（信州大学）、丸山修平氏（金沢大学）との一連の共同研究の話をします。群上の擬準同型（quasimorphism）は双曲幾何などとの関係から大変興味深いものですが、多くの面白い群に対し擬準同型全体のなすベクトル空間がつまらないか無限次元かの二択となってしまいます。1 つの群ではなく群と正規部分群の組の設定で不変擬準同型を考えることで、面白い例で非ゼロな有限次元ベクトル空間を取り出すことができることをお話しします。Bavard の双対定理はこの枠組みに拡張され、この結果は安定交換子長（scl）の粗い幾何（coarse geometry）への応用ももちます。一連の理論の発展をあまり予備知識を仮定せず概観したいと思います。
[ 参考URL ]10/9〜13 の集中講義では Green--Tao の定理とその数体への一般化について話しますが、本講演の内容はそれとは完全に独立しています。川崎盛通氏（北海道大学）、木村満晃氏（京都大学）、松下尚弘氏（信州大学）、丸山修平氏（金沢大学）との一連の共同研究の話をします。群上の擬準同型（quasimorphism）は双曲幾何などとの関係から大変興味深いものですが、多くの面白い群に対し擬準同型全体のなすベクトル空間がつまらないか無限次元かの二択となってしまいます。1 つの群ではなく群と正規部分群の組の設定で不変擬準同型を考えることで、面白い例で非ゼロな有限次元ベクトル空間を取り出すことができることをお話しします。Bavard の双対定理はこの枠組みに拡張され、この結果は安定交換子長（scl）の粗い幾何（coarse geometry）への応用ももちます。一連の理論の発展をあまり予備知識を仮定せず概観したいと思います。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年07月04日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
野坂 武史 氏 (東京工業大学)
３次元多様体のChern-Simons不変量の相互律 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
野坂 武史 氏 (東京工業大学)
３次元多様体のChern-Simons不変量の相互律 (JAPANESE)
[ 講演概要 ]
$M$を閉３次元多様体とする。$M$の基本群から$SL_2(\mathbb{C})$への群準同型（ないし平坦$G$束）に対してChern-Simons不変量や随伴トーションが定まる。多くの既存の研究では、一つの準同型に固定するかCSの臨界点がよく扱われてきた。近年、数理物理で随伴トーションに関し全ての群準同型に対する和を考え、相互律が予想されている。その類似として講演者はCS不変量に関しても同様の和を考察し、その和の２４倍が消える予想を提起した。ある特定の多様体に対し代数$K_3$群の議論を用いる事で予想が正しい事を示せた。本講演では背景や結果の証明の概略を説明する。
[ 参考URL ]$M$を閉３次元多様体とする。$M$の基本群から$SL_2(\mathbb{C})$への群準同型（ないし平坦$G$束）に対してChern-Simons不変量や随伴トーションが定まる。多くの既存の研究では、一つの準同型に固定するかCSの臨界点がよく扱われてきた。近年、数理物理で随伴トーションに関し全ての群準同型に対する和を考え、相互律が予想されている。その類似として講演者はCS不変量に関しても同様の和を考察し、その和の２４倍が消える予想を提起した。ある特定の多様体に対し代数$K_3$群の議論を用いる事で予想が正しい事を示せた。本講演では背景や結果の証明の概略を説明する。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年06月20日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Arnaud Maret 氏 (Sorbonne Université)
Moduli spaces of triangle chains (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Arnaud Maret 氏 (Sorbonne Université)
Moduli spaces of triangle chains (ENGLISH)
[ 講演概要 ]
In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.
[ 参考URL ]In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年06月13日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
臼杵 峻亮 氏 (京都大学)
On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
臼杵 峻亮 氏 (京都大学)
On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)
[ 講演概要 ]
Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.
[ 参考URL ]Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年06月06日(火)
17:30-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
Lie 群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
笹木 集夢 氏 (東海大学)
簡約型球等質空間における可視的作用と不変測度 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie 群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
笹木 集夢 氏 (東海大学)
簡約型球等質空間における可視的作用と不変測度 (JAPANESE)
[ 講演概要 ]
小林俊行氏によって創始された無重複性の伝播定理により，これまで発見されていた無重複表現において表現の無重複性に対する統一的な説明を与えられ，一方で無重複表現の新しい例が系統的に発見された．この定理における本質的な条件として，小林氏は複素多様体における可視的作用の理論を提唱した．可視的作用の概念は，無重複性の伝播定理において重要な役割を果たすだけでなく，群や等質空間に関する新しい分解定理を生み出している．
本講演では，簡約型球等質空間における可視的作用について解説する．特に，可視的に作用するときに各軌道と交叉する部分多様体（スライス）を簡約型球等質空間に対するカルタン分解により構成されることについてお話する．また，この研究の応用として簡約型球等質空間の不変測度に関してカルタン分解に即した積分公式を明示的に与えることにより行う．
[ 参考URL ]小林俊行氏によって創始された無重複性の伝播定理により，これまで発見されていた無重複表現において表現の無重複性に対する統一的な説明を与えられ，一方で無重複表現の新しい例が系統的に発見された．この定理における本質的な条件として，小林氏は複素多様体における可視的作用の理論を提唱した．可視的作用の概念は，無重複性の伝播定理において重要な役割を果たすだけでなく，群や等質空間に関する新しい分解定理を生み出している．
本講演では，簡約型球等質空間における可視的作用について解説する．特に，可視的に作用するときに各軌道と交叉する部分多様体（スライス）を簡約型球等質空間に対するカルタン分解により構成されることについてお話する．また，この研究の応用として簡約型球等質空間の不変測度に関してカルタン分解に即した積分公式を明示的に与えることにより行う．
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年05月30日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
児玉 悠弥 氏 (東京都立大学)
p-colorable subgroup of Thompson's group F (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
児玉 悠弥 氏 (東京都立大学)
p-colorable subgroup of Thompson's group F (JAPANESE)
[ 講演概要 ]
Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.
[ 参考URL ]Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年05月16日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
山下 真由子 氏 (京都大学)
Anderson self-duality of topological modular forms and heretoric string theory (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
山下 真由子 氏 (京都大学)
Anderson self-duality of topological modular forms and heretoric string theory (JAPANESE)
[ 講演概要 ]
Topological Modular Forms (TMF) is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work with Y. Tachikawa, we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. In this talk, I explain our recent update on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways.
[ 参考URL ]Topological Modular Forms (TMF) is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work with Y. Tachikawa, we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. In this talk, I explain our recent update on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年05月09日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
和久井 道久 氏 (関西大学)
結び目とフリーズパターン (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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和久井 道久 氏 (関西大学)
結び目とフリーズパターン (JAPANESE)
[ 講演概要 ]
小木曽岳義氏（城西大学）との共同研究）ConwayとCoxeterは1970年代初頭に、ユニモジュラー規則 ad-bc=1 に基づいて自然数を配置することで生成される数の繰り返し模様（フリーズパターン）を考察し、それが凸多角形の三角形分割により分類されることを示した。現在、フリーズパターンは2000年初頭にFominとZelevinskyにより発見されたクラスター代数との結びつきから再び注目を集めている。
講演者は城西大学の小木曽岳義氏と共同で、京都産業大学の山田修司氏により導入された有理数の祖先三角形の観点から有理絡み目とConway-Coxeterフリーズとの関係を研究し、有理絡み目がConway-Coxeterフリーズにより特徴づけられることを示した。ほぼ同時期に、Morier-GenoudとOvsienkoらも有理数の連分数展開に基づいたq変形を導入し、関連する結果を導いている。本講演ではこれらの結果を概説する。
[ 参考URL ]小木曽岳義氏（城西大学）との共同研究）ConwayとCoxeterは1970年代初頭に、ユニモジュラー規則 ad-bc=1 に基づいて自然数を配置することで生成される数の繰り返し模様（フリーズパターン）を考察し、それが凸多角形の三角形分割により分類されることを示した。現在、フリーズパターンは2000年初頭にFominとZelevinskyにより発見されたクラスター代数との結びつきから再び注目を集めている。
講演者は城西大学の小木曽岳義氏と共同で、京都産業大学の山田修司氏により導入された有理数の祖先三角形の観点から有理絡み目とConway-Coxeterフリーズとの関係を研究し、有理絡み目がConway-Coxeterフリーズにより特徴づけられることを示した。ほぼ同時期に、Morier-GenoudとOvsienkoらも有理数の連分数展開に基づいたq変形を導入し、関連する結果を導いている。本講演ではこれらの結果を概説する。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年04月25日(火)
17:00-18:00 オンライン開催
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野澤 啓 氏 (立命館大学)
Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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野澤 啓 氏 (立命館大学)
Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)
[ 講演概要 ]
We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.
[ 参考URL ]We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年04月18日(火)
17:00-18:00 オンライン開催
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丸山 修平 氏 (中央大学)
A crossed homomorphism on a big mapping class group (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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丸山 修平 氏 (中央大学)
A crossed homomorphism on a big mapping class group (JAPANESE)
[ 講演概要 ]
Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.
[ 参考URL ]Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年04月11日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
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葉廣 和夫 氏 (東京大学大学院数理科学研究科)
On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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葉廣 和夫 氏 (東京大学大学院数理科学研究科)
On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)
[ 講演概要 ]
By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
[ 参考URL ]By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年01月17日(火)
17:00-18:00 オンライン開催
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Chenghan Zha 氏 (東京大学大学院数理科学研究科)
Integral structures in the local algebra of a singularity (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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Chenghan Zha 氏 (東京大学大学院数理科学研究科)
Integral structures in the local algebra of a singularity (ENGLISH)
[ 講演概要 ]
We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
[ 参考URL ]We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年01月10日(火)
17:00-18:00 オンライン開催
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浅香 猛 氏 (東京大学大学院数理科学研究科)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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浅香 猛 氏 (東京大学大学院数理科学研究科)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
[ 講演概要 ]
Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
[ 参考URL ]Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年12月13日(火)
17:30-18:30 オンライン開催
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服部 広大 氏 (慶應義塾大学)
Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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服部 広大 氏 (慶應義塾大学)
Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
[ 講演概要 ]
In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
[ 参考URL ]In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年12月06日(火)
17:00-18:00 オンライン開催
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Quentin Faes 氏 (東京大学大学院数理科学研究科)
Torsion in the abelianization of the Johnson kernel (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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Quentin Faes 氏 (東京大学大学院数理科学研究科)
Torsion in the abelianization of the Johnson kernel (ENGLISH)
[ 講演概要 ]
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.
[ 参考URL ]The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月29日(火)
17:00-18:00 オンライン開催
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黒木 慎太郎 氏 (岡山理科大学)
GKM graph with legs and graph equivariant cohomology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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黒木 慎太郎 氏 (岡山理科大学)
GKM graph with legs and graph equivariant cohomology (JAPANESE)
[ 講演概要 ]
A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).
[ 参考URL ]A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月22日(火)
17:00-18:00 オンライン開催
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北野 晃朗 氏 (創価大学)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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北野 晃朗 氏 (創価大学)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
[ 講演概要 ]
A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
[ 参考URL ]A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月15日(火)
17:00-18:00 オンライン開催
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Arthur Soulié 氏 (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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Arthur Soulié 氏 (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
[ 講演概要 ]
The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
[ 参考URL ]The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月08日(火)
17:00-18:00 オンライン開催
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吉永 正彦 氏 (大阪大学)
Milnor fibers of hyperplane arrangements (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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吉永 正彦 氏 (大阪大学)
Milnor fibers of hyperplane arrangements (JAPANESE)
[ 講演概要 ]
A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
[ 参考URL ]A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月01日(火)
17:00-18:00 オンライン開催
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キム ミンギュ 氏 (東京大学大学院数理科学研究科)
An obstruction problem associated with finite path-integral (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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キム ミンギュ 氏 (東京大学大学院数理科学研究科)
An obstruction problem associated with finite path-integral (JAPANESE)
[ 講演概要 ]
Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
[ 参考URL ]Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年10月25日(火)
17:00-18:00 オンライン開催
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小川 竜 氏 (東海大学)
Stabilized convex symplectic manifolds are Weinstein (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
小川 竜 氏 (東海大学)
Stabilized convex symplectic manifolds are Weinstein (JAPANESE)
[ 講演概要 ]
There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.
[ 参考URL ]There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
