Speaker | Yohsuke Matsuzawa(Osaka Metropolitan University) |

Title | Zariski dense orbit conjecture and arithmetic degree |

Date | October 20 (Thu.) 2022, 17：00～18：00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on October 19th.） |

Abstract | In arithmetic dynamics, people study the arithmetic properties of orbits of rational points (or more generally points with coordinates in algebraic numbers) under self-maps on algebraic varieties. One of the most challenging problems in this field is the so called Zariski dense orbit conjecture, which is about the existence of Zariski dense orbits with coordinates in algebraic numbers. Recently, in a joint work with Long Wang, we proved this conjecture for a certain class of rational maps on projective varieties including birational maps on surfaces. Starting from brief introduction to arithmetic dynamics, I will be talking about this result. |

Speaker | Hirokazu Ninomiya (Meiji University) |

Title | Japanese page only |

Date | September 22 (Thu.) 2022, 16:15〜 |

Place | Lecture Room 228, Building A13 Nakamozu Campus&Zoom |

Abstract | Japanese page only |

Speaker | Tatsuki Kawakami (Ryukoku University) |

Title | Japanese page only |

Date | September 8 (Thu.) 2022, 16:15〜 |

Place | Lecture Room 228, Building A13 Nakamozu Campus&Zoom |

Abstract | Japanese page only |

Speaker | Masatoshi NOUMI (Department of Mathematics, Rikkyo University) |

Title | Elliptic van Diejen difference operators and elliptic hypergeometric integrals of Selberg type |

Date | August 9 (Tue.) 2022, 17:00〜18:00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on August 8th.） |

Abstract | In this talk, I propose a class of eigenfunctions for the elliptic van Diejen operators
(Ruijsenaars operators of type BC) which are represented by elliptic hypergeometric
integrals of Selberg type. They are constructed from simple seed eigenfunctions
by integral transformations, thanks to gauge symmetries and kernel function identities
of the van Diejen operators. This talk is based on a collaboration with Farrok Atai (University of Leeds, UK). |

Speaker | Ayumu Inoue (Department of Mathematics, Tsuda University) |

Title | Introduction to quandle theory, from the aspect of a language for symmetries |

Date | July 12 (Tue.) 2022, 16:00〜17:00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on July 11th.） |

Abstract | A quandle is an algebraic system, which is a non-empty set equipped with a binary operation satisfying several axioms. It is well-known that this algebra has good chemistry with knot theory, because the axioms are closely related to the Reidemeister moves which are fundamental local moves of knot diagrams. On the other hand, it seems to be lesser-known that this algebra also has high compatibility with symmetries. While a group describes whole symmetries of an object, a quandle does some limited symmetries of those. In this talk, the speaker introduces quandle theory from the aspect of a language for symmetries. |

Speaker | Masahiro Morimoto (OCAMI) |

Title | Minimal PF submanifolds in Hilbert spaces with symmetries |

Date | April 26 (Tue.) 2022, 17:00〜18:00 |

Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on April 25th.） |

Abstract | In 1988, R. S. Palais and C.-L. Terng introduced the concept of proper Fredholm (PF) submanifolds in Hilbert spaces. These are submanifolds in separable Hilbert spaces which have finite codimensions and generalize properly immersed submanifolds in Euclidean spaces. By definition the shape operators of PF submanifolds are compact self-adjoint operators. Moreover the infinite dimensional differential topology and Morse theory can be applied to PF submanifolds. Afterwards G. Thorbergsson, E. Heintze and other geometers studied PF submanifolds. They gave interesting applications of PF submanifolds to the finite dimensional submanifold geometry and showed a close relationship with the so-called affine Kac-Moody symmetric spaces. Nowadays PF submanifolds are known as an important research object in geometry. In this talk, I will talk about my research results concerning proper Fredholm submanifolds which are minimal and having certain symmetries. |

Speaker | Yoshinori Hashimoto (Osaka Metropolitan University) |

Title | Canonical metrics, Geometric Invariant Theory, and the Bergman kernel |

Date | April 26 (Tue.) 2022, 15:45〜16:45 |

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

Abstract | Finding a canonical Riemannian metric that has special curvature properties is a natural and important question in differential geometry, and often amounts to solving a nonlinear PDE. A mantra propounded by Atiyah-Bott, Fujiki, and Donaldson states that the curvature of smooth complex projective varieties is an infinite dimensional moment map, and hence canonical metrics can be formulated as a zero of a moment map. On the other hand, the Kempf-Ness theorem states that a zero of a moment map is stable in the sense of Geometric Invariant Theory, indicating a connection between canonical metrics and stability notions in algebraic geometry. This colloquium talk aims to be an informal survey of (a part of) this area of research, highlighting the role played by a complex analytic object called the Bergman kernel and heavily biased towards the work that I have done. Part of the results presented in this talk is based on a joint work with Julien Keller. |

Last Modified on 2022.10.17