Speaker | Hideo Kozono (Waseda University) |

Title | Method of Besov spaces and the Navier-Stokes equations |

Date | October 25 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | We first introduce several basic notions of the Basov spaces such as paraproduct formula and the chain rule. The bilinear estimates related to the nonlinear structure on the Navier-Stokes equations and the $L^p-L^q$-type estimates of the Stokes semigroup are established. Then the problem on existence, uniqueness and regularity of the Navier-Stokes equations is discussed in the scaling invariant homogeneous Besov space. This is based on the joint work with Prof. Senjo Shimizu at Kyoto University. |

Speaker | Noriyuki Abe (Hokkaido University) |

Title | Homological structures of representations |

Date | October 18 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | A linear action of a group (or a Lie algebra) is called a representation. To study representations, we have two steps: first we classify irreducible representations which are building blocks of representations and next we consider how a given representation is built up. For answering the second question, sometimes "grading" structure is useful. I will explain this mechanism and give examples. |

Speaker | Yasuhiro Nakagawa (Saga University) |

Title | On the exsitence problems for Kähler-Ricci solitons on certain toric bundles |

Date | July 12 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | On the certain toric bundles, fiber spaces over Einstein-Kähler Fano manifolds whose fibers are toric Fano manifolds satisfying some conditions, we consider the existence problems for Einstein-Kähler metrics and Kähler-Ricci solitons, and propose some conjectures. We shall explain some examples on which these conjectures holds. |

Speaker | Hideo Takioka (OCAMI) |

Title | Infinitely many knots with the trivial $(2,1)$-cable $\Gamma$-polynomial |

Date | June 28 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | It is known that there exist many polynomial invariants for knots. For example, Alexander-Conway, Jones, $\Gamma$, $Q$, HOMFLYPT, Kauffman polynomials are well known. These polynomials of the trivial knot are one. The problem is whether there exists a non-trivial knot such that these polynomials are one. It is known that there exists such a knot for the Alexander-Conway, $\Gamma$, $Q$ polynomials. However, it is still an open problem for the other polynomial invariants. Moreover, we consider the $(p,1)$-cable versions of these polynomial invariants for an integer $p(\geq 2)$. These $(p,1)$-cable versions of the trivial knot are one. The problem is whether there exists a non-trivial knot such that these $(p,1)$-cable versions are one. It is known that there exists such a knot for the Alexander-Conway polynomial. However, it is still an open problem for the other polynomial invariants. In this talk, we show that there exist infinitely many knots such that the $(2,1)$-cable version of the $\Gamma$-polynomial for the knots is one. |

Speaker | Junjiro Noguchi (U.T./T.I.T. Emeritus) |

Title | Weak Coherence Theorem and Levi's Problem |

Date | May 24 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | pdf file |

Speaker | Ken Abe (Osaka City University) |

Title | Analysis of the Navier-Stokes equations in a space of bounded functions |

Date | April 19 (Wed.) 2017, 16:30〜17:30 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 |

Abstract | The initial-boundary value problem of the Navier-Stokes equations has been studied in a large literature in spaces of integrable functions, while few results are known in a space of bounded functions on which singular integral operators may not act as a bounded operator. In this talk, we introduce some local existence theorem in a space of bounded functions for domains such as bounded or exterior domains. This in particular implies that a minimum rate of potential singularities is type I even in the presence of boundaries. |

Last Modified on 2017.9.21