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Tuesday Seminar on Topology
Seminar information archive ～01/17｜Next seminar｜Future seminars 01/18～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
Seminar information archive
2025/01/14
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Leo Yoshioka (The University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Leo Yoshioka (The University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
[ Abstract ]
In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
[ Reference URL ]In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/12/17
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
[ Abstract ]
In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
[ Reference URL ]In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/12/10
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
[ Abstract ]
Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
[ Reference URL ]Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/12/03
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Jun-ichi Inoguchi (Hokkaido University)
Surfaces in 3-dimensional spaces and Integrable systems (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jun-ichi Inoguchi (Hokkaido University)
Surfaces in 3-dimensional spaces and Integrable systems (JAPANESE)
[ Abstract ]
Surfaces of constant mean curvature in hyperbolic 3-space have different aspects depending on the value of mean curvature. In particular, the class of surfaces of constant mean curvature $H<1$ has no Euclidean or spherical correspondents. I would explain how to construct surface of constant mean curvature $H<1$ in hyperbolic 3-space by the method of Integrable Systems (joint work with Josef F. Dorfmeister and Shinpei Kobayashi).
[ Reference URL ]Surfaces of constant mean curvature in hyperbolic 3-space have different aspects depending on the value of mean curvature. In particular, the class of surfaces of constant mean curvature $H<1$ has no Euclidean or spherical correspondents. I would explain how to construct surface of constant mean curvature $H<1$ in hyperbolic 3-space by the method of Integrable Systems (joint work with Josef F. Dorfmeister and Shinpei Kobayashi).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/26
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Masaki Natori (The University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masaki Natori (The University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence (JAPANESE)
[ Abstract ]
The bulk-edge correspondence refers to the phenomenon typically found in topological insulators, where the topological restriction of the bulk (interior) determines the physical state, such as electric currents, at the edge (boundary). In this talk, we focus on the formulation by G. M. Graf and M. Porta and later by S. Hayashi and provide a new proof of bulk-edge correspondence. It is more direct compared to previous approaches. Behind the proof lies the Bott periodicity of K-theory. The proof of Bott periodicity has been approached from various perspectives. We provide a new proof of Bott periodicity. In the proof, we use Quot schemes in algebraic geometry as configuration spaces.
[ Reference URL ]The bulk-edge correspondence refers to the phenomenon typically found in topological insulators, where the topological restriction of the bulk (interior) determines the physical state, such as electric currents, at the edge (boundary). In this talk, we focus on the formulation by G. M. Graf and M. Porta and later by S. Hayashi and provide a new proof of bulk-edge correspondence. It is more direct compared to previous approaches. Behind the proof lies the Bott periodicity of K-theory. The proof of Bott periodicity has been approached from various perspectives. We provide a new proof of Bott periodicity. In the proof, we use Quot schemes in algebraic geometry as configuration spaces.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/19
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
[ Abstract ]
One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
[ Reference URL ]One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/12
17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
[ Abstract ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
[ Reference URL ]From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/05
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Jun Murakami (Waseda University)
On complexified tetrahedrons associated with the double twist knots and its application to the volume conjecture (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jun Murakami (Waseda University)
On complexified tetrahedrons associated with the double twist knots and its application to the volume conjecture (JAPANESE)
[ Abstract ]
In this talk, I first would like to explain complexified tetrahedrons which subdivide the complement of a double twist knot, and then talk about their application to the volume conjecture. Complexified tetrahedrons are introduced by using the fundamental group, and they are deformations of the regular ideal octahedron which is a half of the complement of the Borromean rings. Such deformations correspond to the surgeries of the Borromean rings producing the double twist knots.
On the other hand, the colored Jones polynomials of the double twist knots are given by the quantum 6j symbol with some extra terms. We see the correspondence of the quantum 6j symbol and the volume of a complexified terahedron by using the Neumann-Zagier function, and we can apply such correspondence to prove the volume conjecture for the double twist knots. To do this, the ADO invariant is used instead of the colored Jones invariant. The l'Hopital's rule is applied to get the ADO invariant, and integral by parts solves the big cancellation problem. At the last, it is shown that the application of the saddle point method is not so hard for this case.
[ Reference URL ]In this talk, I first would like to explain complexified tetrahedrons which subdivide the complement of a double twist knot, and then talk about their application to the volume conjecture. Complexified tetrahedrons are introduced by using the fundamental group, and they are deformations of the regular ideal octahedron which is a half of the complement of the Borromean rings. Such deformations correspond to the surgeries of the Borromean rings producing the double twist knots.
On the other hand, the colored Jones polynomials of the double twist knots are given by the quantum 6j symbol with some extra terms. We see the correspondence of the quantum 6j symbol and the volume of a complexified terahedron by using the Neumann-Zagier function, and we can apply such correspondence to prove the volume conjecture for the double twist knots. To do this, the ADO invariant is used instead of the colored Jones invariant. The l'Hopital's rule is applied to get the ADO invariant, and integral by parts solves the big cancellation problem. At the last, it is shown that the application of the saddle point method is not so hard for this case.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/29
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Takahito Naito (Nippon Institute of Technology)
Cartan calculus in string topology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takahito Naito (Nippon Institute of Technology)
Cartan calculus in string topology (JAPANESE)
[ Abstract ]
The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
[ Reference URL ]The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/22
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Tatsuki Kuwagaki ( Kyoto University)
On the generic existence of WKB spectral networks/Stokes graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsuki Kuwagaki ( Kyoto University)
On the generic existence of WKB spectral networks/Stokes graphs (JAPANESE)
[ Abstract ]
The foliation determined by a quadratic differential on a Riemann surface is a classical object of study. In particular, considering leaves through zero points has been of interest in connection with WKB analysis, Teichmüller theory, and quantum field theory. WKB spectral network (or Stokes graph) is a higher-order-differential version of this notion. In this talk, I will discuss the proof of existence of WKB spectral network for a large class of differentials. If time permits, I will explain its relationship with Lagrangian intersection Floer theory.
[ Reference URL ]The foliation determined by a quadratic differential on a Riemann surface is a classical object of study. In particular, considering leaves through zero points has been of interest in connection with WKB analysis, Teichmüller theory, and quantum field theory. WKB spectral network (or Stokes graph) is a higher-order-differential version of this notion. In this talk, I will discuss the proof of existence of WKB spectral network for a large class of differentials. If time permits, I will explain its relationship with Lagrangian intersection Floer theory.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/17
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Makoto Enokizono (The University of Tokyo)
Slope inequalities for fibered complex surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Makoto Enokizono (The University of Tokyo)
Slope inequalities for fibered complex surfaces (JAPANESE)
[ Abstract ]
Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
[ Reference URL ]Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/08
17:00-18:30 Room #ハイブリッド開催/123 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Hokuto Konno (The University of Tokyo)
Dehn twists on 4-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hokuto Konno (The University of Tokyo)
Dehn twists on 4-manifolds (JAPANESE)
[ Abstract ]
Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
[ Reference URL ]Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/07/23
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Keiko Kawamuro (University of Iowa)
Shortest word problem in braid theory (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Keiko Kawamuro (University of Iowa)
Shortest word problem in braid theory (JAPANESE)
[ Abstract ]
Given a braid element in B_n, searching for a shortest braid word representative (using the band-generators) is called the Shortest Braid Problem. Up to braid index n = 4, this problem has been solved by Kang, Ko, and Lee in 1997. In this talk I will discuss recent development of this problem for braid index 5 or higher. I will also show diagrammatic computational technique of the Left Canonical Form of a given braid, that is a key to the three fundamental problems in braid theory; the Word Problem, the Conjugacy Problem and the Shortest Word Problem. This is joint work with Rebecca Sorsen and Michele Capovilla-Searle.
[ Reference URL ]Given a braid element in B_n, searching for a shortest braid word representative (using the band-generators) is called the Shortest Braid Problem. Up to braid index n = 4, this problem has been solved by Kang, Ko, and Lee in 1997. In this talk I will discuss recent development of this problem for braid index 5 or higher. I will also show diagrammatic computational technique of the Left Canonical Form of a given braid, that is a key to the three fundamental problems in braid theory; the Word Problem, the Conjugacy Problem and the Shortest Word Problem. This is joint work with Rebecca Sorsen and Michele Capovilla-Searle.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/07/09
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Inasa Nakamura (Saga University)
Knitted surfaces in the 4-ball and their chart description (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Inasa Nakamura (Saga University)
Knitted surfaces in the 4-ball and their chart description (JAPANESE)
[ Abstract ]
Knits (or BMW tangles) are tangles in a cylinder generated by generators of the BMW (Birman-Murakami-Wenzl) algebras, consisting of standard generators of the braid group and their inverses, and splices of crossings called pairs of hooks. We give a new construction of surfaces in $D^2 \times B^2$, called knitted surfaces (or BMW surfaces), that are described as the trace of deformations of knits, and we give the notion of charts for knitted surfaces, that are finite graphs in $B^2$. We show that a knitted surface has a chart description. Knitted surfaces and their chart description include 2-dimensional braids and their chart description. This is joint work with Jumpei Yasuda (Osaka University).
[ Reference URL ]Knits (or BMW tangles) are tangles in a cylinder generated by generators of the BMW (Birman-Murakami-Wenzl) algebras, consisting of standard generators of the braid group and their inverses, and splices of crossings called pairs of hooks. We give a new construction of surfaces in $D^2 \times B^2$, called knitted surfaces (or BMW surfaces), that are described as the trace of deformations of knits, and we give the notion of charts for knitted surfaces, that are finite graphs in $B^2$. We show that a knitted surface has a chart description. Knitted surfaces and their chart description include 2-dimensional braids and their chart description. This is joint work with Jumpei Yasuda (Osaka University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/07/02
17:00-18:30 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kokoro Tanaka (Tokyo Gakugei University)
The second quandle homology group of the knot $n$-quandle (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kokoro Tanaka (Tokyo Gakugei University)
The second quandle homology group of the knot $n$-quandle (JAPANESE)
[ Abstract ]
We compute the second quandle homology group of the knot $n$-quandle for each integer $n>1$, where the knot $n$-quandle is a certain quotient of the knot quandle (of an oriented classical knot in the $3$-sphere). Although the second quandle homology group of the knot quandle can only detect the unknot, it turns out that that of its 3-quandle can detect the unknot, the trefoil and the cinqfoil. This is a joint work with Yuta Taniguchi.
[ Reference URL ]We compute the second quandle homology group of the knot $n$-quandle for each integer $n>1$, where the knot $n$-quandle is a certain quotient of the knot quandle (of an oriented classical knot in the $3$-sphere). Although the second quandle homology group of the knot quandle can only detect the unknot, it turns out that that of its 3-quandle can detect the unknot, the trefoil and the cinqfoil. This is a joint work with Yuta Taniguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/25
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Emmy Murphy (University of Toronto)
Liouville symmetry groups and pseudo-isotopies (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Emmy Murphy (University of Toronto)
Liouville symmetry groups and pseudo-isotopies (ENGLISH)
[ Abstract ]
Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.
[ Reference URL ]Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/20
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
[ Abstract ]
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
[ Reference URL ]The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/11
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
[ Abstract ]
Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
[ Reference URL ]Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/04
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
[ Abstract ]
The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
[ Reference URL ]The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/28
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
[ Abstract ]
The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
[ Reference URL ]The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/21
17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yuichi Ike (Institute of Mathematics for Industry, Kyushu University)
γ-supports and sheaves (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yuichi Ike (Institute of Mathematics for Industry, Kyushu University)
γ-supports and sheaves (JAPANESE)
[ Abstract ]
The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).
[ Reference URL ]The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/14
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Noriyuki Hamada (Institute of Mathematics for Industry, Kyushu University)
Exotic 4-manifolds with signature zero (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Noriyuki Hamada (Institute of Mathematics for Industry, Kyushu University)
Exotic 4-manifolds with signature zero (JAPANESE)
[ Abstract ]
We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.
This is joint work with Inanc Baykur (University of Massachusetts Amherst).
[ Reference URL ]We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.
This is joint work with Inanc Baykur (University of Massachusetts Amherst).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/07
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
The Thurston spine and the Systole function of Teichmüller space (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
The Thurston spine and the Systole function of Teichmüller space (ENGLISH)
[ Abstract ]
The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.
[ Reference URL ]The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/04/23
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó $d$-invariants of Brieskorn homology 3-spheres (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó $d$-invariants of Brieskorn homology 3-spheres (JAPANESE)
[ Abstract ]
This talk consists of the following two research contents:
I. The boundary sum of $S^1 \times D^3$ and $D^2 \times S^2$ is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette $P$ embedded in a 4-manifold $X$, a pochette surgery on $X$ is the operation of removing the interior of $P$ and gluing $P$ by a diffeomorphism of the boundary of $P$. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a $d$-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
[ Reference URL ]This talk consists of the following two research contents:
I. The boundary sum of $S^1 \times D^3$ and $D^2 \times S^2$ is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette $P$ embedded in a 4-manifold $X$, a pochette surgery on $X$ is the operation of removing the interior of $P$ and gluing $P$ by a diffeomorphism of the boundary of $P$. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a $d$-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/04/16
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Hiroaki Karuo (Gakushuin University)
Skein algebras and quantum tori in view of pants decompositions (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hiroaki Karuo (Gakushuin University)
Skein algebras and quantum tori in view of pants decompositions (JAPANESE)
[ Abstract ]
To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger--Yang skein algebras of punctured surfaces.
In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger--Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).
[ Reference URL ]To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger--Yang skein algebras of punctured surfaces.
In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger--Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
