Organizers: Airi Aso

Schedule of Upcoming Seminar

December 16 John Parker (Durham Univ.)

January 27 Hidetoshi Masai (Tokyo Institute of Technology )

Speaker | Hidetoshi Masai (Tokyo Institute of Technology ) |

Title | Visualizing deformations of hyperbolic and complex structures on 4-punctured spheres. |

Date | January 27 (Fri.) 16：00～17：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., F415 & Zoom |

Abstract | We present movies and pictures of hyperbolic and complex structures on 4-punctured spheres. The deformation space of both structures is known as Teichmueller space, and there are several natural paths that capture natural deformations of hyperbolic and complex structures. For example, Teichmueller geodesics and earthquake deformations will be discussed. I will also talk about the motivations of those drawings in relation to hyperbolic volumes of fibered manifolds e.g. the fibered closure of braids of 3 strands. |

Speaker | John Parker (Durham Univ.) |

Title | Margulis regions for screw-parabolic maps |

Date | December 16 (Fri.) 16：00～17：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., F415 & Zoom |

Abstract | A famous result of Margulis says that there is a universal constant only depending on dimension with the following property. If G is a discrete group of hyperbolic isometries and x is a point then the elements of G that displace x by a distance less than the constant generate a nilpotent group. The thin part of the quotient orbifold is the collection of points where this nilpotent group is infinite. In this talk I will discuss the shape of the this part of a hyperbolic 4-manifold close associated to a screw-parabolic map with irrational rotational part. This involves results from Diophantine approximation in rather surprising ways. |

Speaker | Wataru Yuasa(OCAMI / RIMS) |

Title | State-clasp correspondence for skein algebras |

Date | December 2 (Fri.) 16：00～17：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., F415 & Zoom |

Abstract | For a compact oriented surface S with special points and intervals onthe boundary, we introduce the stated g-skein algebra and the claspedg-skein algebra of S for g=sp_4. Moreover, we show that the reducedversion of the stated g-skein algebra is isomorphic to theboundary-localization of the clasped g-skein algebra for a Lie algebrag=sl_2, sl_3 or sp_4. This isomorphism is a quantum counterpart of thetwo descriptions of the cluster algebra associated with the pair (g,S)in terms of the matrix coefficients of Wilson lines and cluster variables, respectively. This talk is based on joint work with TsukasaIshibashi (Tohoku Univ.). |

Speaker | Nobutaka Asano (National Institute of Technology, Tsuyama College) |

Title | Some lower bounds for the Kirby-Thompson invariant of 4-manifolds |

Date | November 25 (Fri.) 16：00～17：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., F415 & Zoom |

Abstract | A trisection is a decomposition of a closed 4-manifold X into a 3-tuple of 4-dimensional 1-handlebodies, which was introduced by Gay and Kirby. Kirby and Thompson defined an invariant of X by using trisections. This invariant is called the Kirby-Thompson invariant. In this talk, we give some lower bounds for the Kirby-Thompson invariant of certain 4-manifolds. As an application, we find the first example of a 4-manifold whose Kirby-Thompson invariant is non-zero. This is a joint work with Hironobu Naoe (Chuo University) and Masaki Ogawa (Saitama University). |

Speaker | Erika Kuno (Osaka University) |

Title | Quasi-isometric embeddings induced by the orientation double coverings |

Date | November 18 (Fri.) 16：00～17：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., F415 & Zoom |

Abstract | Birman--Chillingworth firstly proved that each mapping class group of a nonorientable surface is a subgroup of the mapping class group of the doule covering orientable surface. We prove that this natural injective homomorphism is a quasi-isometric embedding by using semihyperbolicity of the (extended) mapping class groups of the orientable surfaces. This is a joint work with Takuya Katayama. |

Speaker | You Hasegawa (Osaka University) |

Title | Gromov boundaries of non-proper hyperbolic geodesic spaces |

Date | October 28 (Fri.)16：00～17：00 |

Abstract | In a proper hyperbolic geodesic space, it is well known that the sequential boundary can be identified as topological spaces with the geodesic boundary. We show that in a (not necessarily proper) hyperbolic geodesic space, the sequential boundary can be identified as topological spaces with the quasi-geodesic boundary. |

Speaker | Hiroaki Karuo (Gakushuin University) |

Title | Quantum trace maps for LRY skein algebras |

Date | July 22 (Fri.)16：00～17：00 |

Abstract | Based on Bonahon and Wong's works, Le formulated stated skein algebras to understand quantum trace maps. On the other hand, Roger--Yang introduced Roger--Yang skein algebras to give an explicit connection between skien algebras and decorated Teichmuller spaces. As a generalization of stated skein algebras and RY skein algebras, one can consider Le--Roger--Yang skein algebras. In this talk, we show the key idea to construct the quantum trace maps for LRY skein algebras and what the LRY skein algebra of an elementary surface is. This is a joint work with W. Bloomquist and Thang T. Q. Le at Georgia Tech. |

Speaker | Yuta Taniguchi(Osaka University) |

Title | The knot quandle of the $n$-twist spun knot is a central extension of the knot $n$-quandle. |

Date | July 8 (Fri.)16：00～17：00 |

Abstract | Given an oriented $m$-knot $K$, we have the knot quandle of $K$, which is an analogy of the knot group of $K$. Inoue showed that the knot quandle of $n$-twist spun trefoil is a central extension of the Schl\"{a}fli quandle related to $\{ 3,n\}$. In this talk, we generalize the Inoue's result. More precisely, we show that for any $1$-knot $K$, the knot quandle of the $n$-twist spun $K$ is a central extension of the knot $n$-quandle of $K$. This is a joint work with Kokoro Tanaka (Tokyo Gakugei University). |

Speaker | Jumpei Yasuda (Osaka University) |

Title | Computation of the knot symmetric quandle and the plat index for surface-links |

Date | July 1 (Fri.)16：00～17：00 |

Abstract | A plat form for links is a presentation of a classical link using a braid. We can apply this presentation to surface-links, using a braided surface instead of a braid, and prove that every surface-link has a plat form presentation. In this talk, we show how to compute the knot symmetric quandle of a surface-link using a plat form.
As an application, for any positive integer m, we give infinitely many surface-knots with the plat index m. |

Speaker | Masaki Ogawa (Saitama University) |

Title | On the reducibility of handlebody decompositions. |

Date | June 17 (Fri.)16：00～17：00 |

Abstract | Haken showed that any Heegaard splittings of reducible 3-manifolds are reducible. This is well-known and called Haken’s lemma.
We can consider a decomposition of a 3-manifold with three handlebodies. We call a such decomposition a handlebody decompositions. This is a generalization of a Heegaard splitting. In this talk, we introduce an operation called a connect sum of a handlebody decomposition. After that, we consider the handlebody decompositions of the connected sum of two lens spaces and show that some of them are obtained by connect summing two handlebody decompositions. |

Speaker | Shin'ya Okazaki (Nara University of Education) |

Title | On the crossing number of constituent links of a handlebody-knot |

Date | June 3 (Fri.)16：00～17：00 |

Abstract | A handlebody-knot is a handlebody embedded in the 3-sphere.
When the genus 2 handlebody-knot is cut open with a separating disk, a two component knotted solid tori appears. This is regarded as a 2-component link and is called a constituent link of the handlebody-knot. In this talk, we introduce a generalization of the degree of Laurent polynomial. We show that the generalized degree of the Alexander polynomial of a pair consisting of a genus 2 handlebody-knot and its meridian system give a lower bound of the crossing number of constituent links of a genus 2 handlebody-knot. |

Speaker | Dounnu Sasaki (Gakushuin University) |

Title | Currents on cusped hyperbolic surfaces and denseness property |

Date | May 13 (Fri.) 16：00～17：00 |

Abstract | The space GC(S) of geodesic currents on a hyperbolic surface S can be considered as a completion of the set of weighted closed geodesics on S when S is compact,
since the set of rational geodesic currents on S, which correspond to weighted closed geodesics, is a dense subset of GC(S). We proved that even when S is a cusped hyperbolic surface with finite area, GC(S) has the denseness property of rational geodesic currents,
which correspond not only to weighted closed geodesics on S but also to weighted geodesics connecting two cusps. In addition, we proved that the space of subset currents on a cusped hyperbolic surface, which is a generalization of geodesic currents,
also has the denseness property of rational subset currents.
In this talk, we will talk about the characterization of rational geodesic currents and subset currents by using basic hyperbolic geometry. |

Last Modified on 2022.12.15

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