本文印刷
全画面プリント
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
2021年07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。
作間 誠 氏 (大阪市立大学数学研究所)
Homotopy motions of surfaces in 3-manifolds (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。
作間 誠 氏 (大阪市立大学数学研究所)
Homotopy motions of surfaces in 3-manifolds (JAPANESE)
[ 講演概要 ]
We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).
[ 参考URL ]We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behaviour of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting. This is a joint work with Yuya Koda (arXiv:2011.05766).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年07月06日(火)
17:30-18:30 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。
窪田 陽介 氏 (信州大学)
Codimension 2 transfer map in higher index theory (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。
窪田 陽介 氏 (信州大学)
Codimension 2 transfer map in higher index theory (JAPANESE)
[ 講演概要 ]
The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
[ 参考URL ]The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年06月29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。
早野 健太 氏 (慶應義塾大学)
Stability of non-proper functions (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。
早野 健太 氏 (慶應義塾大学)
Stability of non-proper functions (JAPANESE)
[ 講演概要 ]
In this talk, we will give a sufficient condition for (strong) stability of non-proper functions (with respect to the Whitney topology). As an application, we will give a strongly stable but not infinitesimally stable function. We will further show that any Nash function on the Euclidean space becomes stable after a generic linear perturbation.
[ 参考URL ]In this talk, we will give a sufficient condition for (strong) stability of non-proper functions (with respect to the Whitney topology). As an application, we will give a strongly stable but not infinitesimally stable function. We will further show that any Nash function on the Euclidean space becomes stable after a generic linear perturbation.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年06月22日(火)
17:00-18:30 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。
小林 竜馬 氏 (石川工業高等専門学校)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (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。
小林 竜馬 氏 (石川工業高等専門学校)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
[ 講演概要 ]
An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
[ 参考URL ]An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年06月15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。
佐藤 尚倫 氏 (早稲田大学)
Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (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。
佐藤 尚倫 氏 (早稲田大学)
Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)
[ 講演概要 ]
In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.
[ 参考URL ]In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年06月08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。
松下 尚弘 氏 (琉球大学)
Graphs whose Kronecker coverings are bipartite Kneser graphs (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。
松下 尚弘 氏 (琉球大学)
Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)
[ 講演概要 ]
Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.
In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.
In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.
[ 参考URL ]Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.
In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.
In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年06月01日(火)
17:30-18:30 オンライン開催
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。
北川 宜稔 氏 (早稲田大学)
On the discrete decomposability and invariants of representations of real reductive Lie groups (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。
北川 宜稔 氏 (早稲田大学)
On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)
[ 講演概要 ]
群の既約表現を部分群に制限したときにどのように振る舞うかを記述する問題を分岐則の問題という。既約表現の制限は一般には既約ではなくなり、ユニタリな場合には直積分で記述される既約分解が存在する。この分解は、ユニタリ作用素のスペクトル分解の一般化とみなすことができ、一般には連続的なスペクトルと離散的なスペクトルが現れる。連続的なスペクトルが現れない場合、つまりユニタリ表現の離散的な直和になっている場合、その表現は離散分解するという。
離散分解する分岐則は技術的に扱いやすいというだけでなく、大きな群の表現の情報から小さい部分群の表現の情報が取り出しやすい状況になっており、以下のような応用が知られている。保型形式から別の保型形式を作り出す Rankin--Cohen ブラケットという作用素は、離散分解する表現から既約表現への絡作用素として得られることが知られており、近年でも多くの一般化が得られている。また、等質空間の L^2 関数の空間の離散スペクトルを別の等質空間のものから構成するという結果にも用いられている。(T. Kobayashi, J. Funct. Anal. ('98))
本講演では、実簡約リー群の既約表現の制限の離散分解性について、小林俊行氏が提唱した離散分解性とG'-許容性の一般論と判定条件(Invent. math. '94, Annals of Math. '98, Invent. math. '98)を踏まえつつ、最近得られた結果を紹介したい。表現の代数的な不変量である随伴多様体、解析的な不変量である wave front set、表現空間の位相、の三つを用いて離散分解性を記述する。
[ 参考URL ]群の既約表現を部分群に制限したときにどのように振る舞うかを記述する問題を分岐則の問題という。既約表現の制限は一般には既約ではなくなり、ユニタリな場合には直積分で記述される既約分解が存在する。この分解は、ユニタリ作用素のスペクトル分解の一般化とみなすことができ、一般には連続的なスペクトルと離散的なスペクトルが現れる。連続的なスペクトルが現れない場合、つまりユニタリ表現の離散的な直和になっている場合、その表現は離散分解するという。
離散分解する分岐則は技術的に扱いやすいというだけでなく、大きな群の表現の情報から小さい部分群の表現の情報が取り出しやすい状況になっており、以下のような応用が知られている。保型形式から別の保型形式を作り出す Rankin--Cohen ブラケットという作用素は、離散分解する表現から既約表現への絡作用素として得られることが知られており、近年でも多くの一般化が得られている。また、等質空間の L^2 関数の空間の離散スペクトルを別の等質空間のものから構成するという結果にも用いられている。(T. Kobayashi, J. Funct. Anal. ('98))
本講演では、実簡約リー群の既約表現の制限の離散分解性について、小林俊行氏が提唱した離散分解性とG'-許容性の一般論と判定条件(Invent. math. '94, Annals of Math. '98, Invent. math. '98)を踏まえつつ、最近得られた結果を紹介したい。表現の代数的な不変量である随伴多様体、解析的な不変量である wave front set、表現空間の位相、の三つを用いて離散分解性を記述する。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年05月25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。
足助 太郎 氏 (東京大学大学院数理科学研究科)
On a characteristic class associated with deformations of foliations (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。
足助 太郎 氏 (東京大学大学院数理科学研究科)
On a characteristic class associated with deformations of foliations (JAPANESE)
[ 講演概要 ]
A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.
[ 参考URL ]A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年05月18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。
Geoffrey Powell 氏 (CNRS and University of Angers)
On derivations of free algebras over an operad and the generalized divergence (ENGLISH)
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。
Geoffrey Powell 氏 (CNRS and University of Angers)
On derivations of free algebras over an operad and the generalized divergence (ENGLISH)
[ 講演概要 ]
This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.
One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.
The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.
[ 参考URL ]This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.
One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.
The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年05月11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。
山下 真由子 氏 (京都大学数理解析研究所)
トポロジカルとは限らない invertible QFT の分類問題と, Anderson dual の differential なモデル (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。
山下 真由子 氏 (京都大学数理解析研究所)
トポロジカルとは限らない invertible QFT の分類問題と, Anderson dual の differential なモデル (JAPANESE)
[ 講演概要 ]
Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. Actually this construction turns out to be mathematically interesting because of its relation with differential cohomology theories. I will start from basic motivations for the classification problem, reportthe progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Tohokku, physics).
[ 参考URL ]Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. Actually this construction turns out to be mathematically interesting because of its relation with differential cohomology theories. I will start from basic motivations for the classification problem, reportthe progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Tohokku, physics).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2021年04月27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。
栗林 勝彦 氏 (信州大学)
On a singular de Rham complex in diffeology (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
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。
栗林 勝彦 氏 (信州大学)
On a singular de Rham complex in diffeology (JAPANESE)
[ 講演概要 ]
Diffeology gives a complete, co-complete, cartesian closed category into which the category of manifolds embeds. In the framework of diffeology, the de Rham complex in the sense of Souriau enables us to develop de Rham calculus. Moreover,Iglesias-Zemmour has been introduced homotopical concepts such as homotopy groups, cubic homology groups and fibrations in diffeology. Thus one might expect `differential homotopy theory'. However, the de Rham theorem does not hold for Souriau's cochain
complex in general. In this talk, I will introduce a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space.
[ 参考URL ]Diffeology gives a complete, co-complete, cartesian closed category into which the category of manifolds embeds. In the framework of diffeology, the de Rham complex in the sense of Souriau enables us to develop de Rham calculus. Moreover,Iglesias-Zemmour has been introduced homotopical concepts such as homotopy groups, cubic homology groups and fibrations in diffeology. Thus one might expect `differential homotopy theory'. However, the de Rham theorem does not hold for Souriau's cochain
complex in general. In this talk, I will introduce a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
2021年04月20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。
大鹿 健一 氏 (学習院大学)
Realisation of measured laminations on boundaries of convex cores (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
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。
大鹿 健一 氏 (学習院大学)
Realisation of measured laminations on boundaries of convex cores (JAPANESE)
[ 講演概要 ]
I shall present a generalisation of the theorem by Bonahon-Otal concerning realisation of measured laminations as bending laminations of geometrically finite groups, to general Kleinian surface groups which might be geometrically infinite. Our proof is based on analysis of geometric limits, and is independent of the technique of hyperbolic cone-manifolds employed by Bonahon-Otal. This is joint work with Shinpei Baba (Osaka Univ.).
[ 参考URL ]I shall present a generalisation of the theorem by Bonahon-Otal concerning realisation of measured laminations as bending laminations of geometrically finite groups, to general Kleinian surface groups which might be geometrically infinite. Our proof is based on analysis of geometric limits, and is independent of the technique of hyperbolic cone-manifolds employed by Bonahon-Otal. This is joint work with Shinpei Baba (Osaka Univ.).
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
2021年04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。
伊藤 哲也 氏 (京都大学)
Quantitative Birman-Menasco theorem and applications to crossing number (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
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。
伊藤 哲也 氏 (京都大学)
Quantitative Birman-Menasco theorem and applications to crossing number (JAPANESE)
[ 講演概要 ]
Birman-Menasco proved that there are finitely many knots having a given genus and braid index. We give a quantitative version of Birman-Menasco finiteness theorem; an estimate of the crossing number of knots in terms of genus and braid index. As applications, we give various supporting evidences of various conjectural properties of the crossing number of knots.
[ 参考URL ]Birman-Menasco proved that there are finitely many knots having a given genus and braid index. We give a quantitative version of Birman-Menasco finiteness theorem; an estimate of the crossing number of knots in terms of genus and braid index. As applications, we give various supporting evidences of various conjectural properties of the crossing number of knots.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj
2021年01月12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。
木村 満晃 氏 (東京大学大学院数理科学研究科)
Bounded cohomology of volume-preserving diffeomorphism groups (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。
木村 満晃 氏 (東京大学大学院数理科学研究科)
Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)
[ 講演概要 ]
Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.
(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.
(2) When the volume of M is infinite.
In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".
[ 参考URL ]Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.
(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.
(2) When the volume of M is infinite.
In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年12月15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。
金 英子 氏 (大阪大学)
Braids, triangles and Lissajous curve (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。
金 英子 氏 (大阪大学)
Braids, triangles and Lissajous curve (JAPANESE)
[ 講演概要 ]
The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.
[ 参考URL ]The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年12月08日(火)
17:30-18:30 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。
佐藤 進 氏 (神戸大学)
The intersection polynomials of a virtual knot (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。
佐藤 進 氏 (神戸大学)
The intersection polynomials of a virtual knot (JAPANESE)
[ 講演概要 ]
We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.
[ 参考URL ]We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年12月01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。
古宇田 悠哉 氏 (広島大学)
Goeritz groups of bridge decompositions (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。
古宇田 悠哉 氏 (広島大学)
Goeritz groups of bridge decompositions (JAPANESE)
[ 講演概要 ]
For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.
[ 参考URL ]For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年11月24日(火)
17:30-18:30 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。
馬場 伸平 氏 (大阪大学)
Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (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。
馬場 伸平 氏 (大阪大学)
Intersection of Poincare holonomy varieties and Bers' simultaneous uniformization theorem (JAPANESE)
[ 講演概要 ]
Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP1-structures on X. Then, by the holonomy representations of CP1-structures, this vector space properly embeds into the PSL(2, C)-character variety, the space of representations of the fundamental group of X into PSL(2,C).
In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP1-structures.
[ 参考URL ]Given a marked compact Riemann surface X, the vector space of holomorphic quadratic differentials on X is identified with the space of CP1-structures on X. Then, by the holonomy representations of CP1-structures, this vector space properly embeds into the PSL(2, C)-character variety, the space of representations of the fundamental group of X into PSL(2,C).
In this manner, different Riemann surfaces structures yield different half-dimensional smooth analytic subvarieties in the character variety. In this talk, we discuss some properties of their intersection. To do so, we utilize a cut-and-paste operation, called grafting, of CP1-structures.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年11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。
三松 佳彦 氏 (中央大学)
Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (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。
三松 佳彦 氏 (中央大学)
Lefschetz fibration on the Milnor fibers of simple elliptic and cusp singularities (JAPANESE)
[ 講演概要 ]
In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.
There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.
An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.
[ 参考URL ]In this talk a joint work with Naohiko Kasuya(Kyoto Sangyo U.), Hiroki Kodama(Tohoku U.), and Atsuhide Mori(Osaka Dental U.) is reported. The main result is the following.
There exist a Lefschetz fibration of the Milnor fiber of T_{pqr}-singularity (1/p + 1/q + 1/r ≦ 1) to the unit disk with regular fiber diffeomorphic to T^2.
An outline of the construction will be explained, through which, the space of 2-jets of (R^4, 0) to (R^2, 0) is analysed. This is motivated by F. Presas' suggestion that the speaker's construction of regular Poisson structures(=leafwise symplectic foliations) on S^5 might be interpreted by ``leafwise Lefschetz fibration''. These Lefschetz fibrations give a way to look at K3 surfaces through an extended class of Arnol'd's strange duality. These applications are introduced as well.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年10月27日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
吉田 純 氏 (東京大学大学院数理科学研究科)
Vassiliev derivatives of Khovanov homology and its application (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、下記URLから参加登録を行って下さい。
吉田 純 氏 (東京大学大学院数理科学研究科)
Vassiliev derivatives of Khovanov homology and its application (JAPANESE)
[ 講演概要 ]
Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.
[ 参考URL ]Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年10月20日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
Alexandru Oancea 氏 (Sorbonne Université)
Poincaré duality for free loop spaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、下記URLから参加登録を行って下さい。
Alexandru Oancea 氏 (Sorbonne Université)
Poincaré duality for free loop spaces (ENGLISH)
[ 講演概要 ]
A certain number of dualities between homological and cohomological invariants of free loop spaces have been observed over the years, having the flavour of Poincaré duality but nevertheless holding in an infinite dimensional setting. The goal of the talk will be to explain these through a new duality theorem, whose proof uses symplectic methods. The talk will report on joint work with Kai Cieliebak and Nancy Hingston.
[ 参考URL ]A certain number of dualities between homological and cohomological invariants of free loop spaces have been observed over the years, having the flavour of Poincaré duality but nevertheless holding in an infinite dimensional setting. The goal of the talk will be to explain these through a new duality theorem, whose proof uses symplectic methods. The talk will report on joint work with Kai Cieliebak and Nancy Hingston.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2020年10月06日(火)
17:30-18:30 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
松尾 信一郎 氏 (名古屋大学)
境界付き多様体の Atiyah-Patodi-Singer の指数とドメインウォールフェルミオン (JAPANESE)
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL
参加を希望される場合は、下記URLから参加登録を行って下さい。
松尾 信一郎 氏 (名古屋大学)
境界付き多様体の Atiyah-Patodi-Singer の指数とドメインウォールフェルミオン (JAPANESE)
[ 講演概要 ]
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index.
In a previous work, motivated by the study of lattice gauge theory, we derived a formula expressing the Atiyah-Patodi-Singer index in terms of the eta invariant of “domain-wall fermion Dirac operators” when the base manifold is a flat 4-dimensional torus. Now we generalise this formula to any even dimensional closed Riemannian manifolds, and prove it mathematically rigorously. Our proof uses a Witten localisation argument combined with a devised embedding into a cylinder of one dimension higher. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.
This talk is based on a joint paper arXiv:1910.01987, to appear in CMP, with H. Fukaya, M. Furuta, T. Onogi, S. Yamaguchi, and M. Yamashita.
[ 参考URL ]We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index.
In a previous work, motivated by the study of lattice gauge theory, we derived a formula expressing the Atiyah-Patodi-Singer index in terms of the eta invariant of “domain-wall fermion Dirac operators” when the base manifold is a flat 4-dimensional torus. Now we generalise this formula to any even dimensional closed Riemannian manifolds, and prove it mathematically rigorously. Our proof uses a Witten localisation argument combined with a devised embedding into a cylinder of one dimension higher. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.
This talk is based on a joint paper arXiv:1910.01987, to appear in CMP, with H. Fukaya, M. Furuta, T. Onogi, S. Yamaguchi, and M. Yamashita.
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL
2020年09月29日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
岩木 耕平 氏 (東京大学大学院数理科学研究科)
Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL
参加を希望される場合は、下記URLから参加登録を行って下さい。
岩木 耕平 氏 (東京大学大学院数理科学研究科)
Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)
[ 講演概要 ]
In 1998, Lawrence-Zagier introduced a certain q-series and proved that its limit value at root of unity q=exp(2π i / K) coincides with the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant of the Poincare homology sphere Σ(2,3,5) at the level K. Employing the idea of Gukov-Marino-Putrov based on resurgent analysis, we generalize the result of Lawrence-Zagier for the Seifert loops (Seifert manifolds with a single loop inside). That is, for each Seifert loop, we introduce an explicit q-series (WRT function) and show that its limit value at the root of unity coincides with the WRT invariant of the Seifert loop. We will also discuss a q-difference equation satisfied by the WRT function. This talk is based on a joint work with H. Fuji, H. Murakami and Y. Terashima which is available on arXiv:2007.15872.
[ 参考URL ]In 1998, Lawrence-Zagier introduced a certain q-series and proved that its limit value at root of unity q=exp(2π i / K) coincides with the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant of the Poincare homology sphere Σ(2,3,5) at the level K. Employing the idea of Gukov-Marino-Putrov based on resurgent analysis, we generalize the result of Lawrence-Zagier for the Seifert loops (Seifert manifolds with a single loop inside). That is, for each Seifert loop, we introduce an explicit q-series (WRT function) and show that its limit value at the root of unity coincides with the WRT invariant of the Seifert loop. We will also discuss a q-difference equation satisfied by the WRT function. This talk is based on a joint work with H. Fuji, H. Murakami and Y. Terashima which is available on arXiv:2007.15872.
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL
2020年07月28日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
Anderson Vera 氏 (京都大学数理解析研究所)
A double filtration for the mapping class group and the Goeritz group of the sphere (ENGLISH)
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ
参加を希望される場合は、下記URLから参加登録を行って下さい。
Anderson Vera 氏 (京都大学数理解析研究所)
A double filtration for the mapping class group and the Goeritz group of the sphere (ENGLISH)
[ 講演概要 ]
I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of $S^3$. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)
[ 参考URL ]I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of $S^3$. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ
2020年07月21日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、下記URLから参加登録を行って下さい。
Sergei Burkin 氏 (東京大学大学院数理科学研究科)
Twisted arrow categories of operads and Segal conditions (ENGLISH)
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ
参加を希望される場合は、下記URLから参加登録を行って下さい。
Sergei Burkin 氏 (東京大学大学院数理科学研究科)
Twisted arrow categories of operads and Segal conditions (ENGLISH)
[ 講演概要 ]
We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category $\Delta$, Segal's category $\Gamma$ and Moerdijk--Weiss category $\Omega$ are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.
[ 参考URL ]We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category $\Delta$, Segal's category $\Gamma$ and Moerdijk--Weiss category $\Omega$ are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ
