# Differential Geometry Seminar (2023)

As a project of OCAMI, we shall promote the seminar on differential geometry in the wide sense of including the areas related to geometric analysis, topology, algebraic geometry, mathematical physics, integrable systems, information sciences etc.

Differential Geometry Seminar (list by year)

#### Differential Geometry Seminar (2023) Talks

Date | February 5 (Mon.) 2024, 16:45-18:15（Japan time） |
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Speaker | Haizhong Li (Tsinghua University) |

Title |
Curvature flows for hypersurfaces and their geometric applications |

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

Abstract |
Isoperimetric inequality is one of the oldest problems in mathematics, which relates with convex geometry, differential geometry and geometric PDEs, etc. Recently, the isoperimetric type inequalities in hyperbolic space have been widely investigated by using the hypersurface curvature flows, including the inverse curvature flows, quermassintegral preserving curvature flows, contracting curvature flows, and locally constrained curvature flows. In this talk, I will survey the recent progress in this direction, which is based on my joint works with Ben Andrews (ANU), Yong Wei (USTC), Changwei Xiong (SCU), Yingxiang Hu (Beihang U.). |

Date | December 1 (Fri.) 2023, 16:45-18:15（Japan time） |
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Speaker | Takahiro Aoi (National Institute of Technology, Wakayama College) |

Title |
A conical approximation of constant scalar curvature Kähler metrics of Poincaré type and algebro-geometric stability |

Place | Faculty of Science Bldg., E101 |

Date | November 10 (Fri.) 2023, 16:45-18:15（Japan time） |
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Speaker | Natsuo Miyatake (Mathematical Science Center for Co-creative Society, Tohoku University) |

Title |
Extended Hitchin equation for cyclic Higgs bundles associated with a quasi-subharmonic function, and its Dirichlet problem |

Place | Faculty of Science Bldg., E211 |

Date | November 9 (Thu.) 2023, 13:30-14:30（Japan time） |
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Speaker | Michael Pevzner（Reims University） |

Title |
Generating operators for symmetry breaking |

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

Abstract |
We introduce the notion of "generating operator" for a family of differential operators between two manifolds and develop this construction in the framework of covariant differential operators acting on sections of holomorphic vector bundles over homogeneous spaces. An explicit formula for the generating operator associated with the Rankin--Cohen brackets will be discussed. |

Date | October 27 (Fri.) 2023, 16:45-18:15（Japan time） |
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Speaker | Yoshinori Hashimoto (Osaka Metropolitan University) |

Title |
A Hilbert-Mumford criterion for nilsolitons |

Place | Faculty of Science Bldg., E101 |

Date | July 21 (Fri.) 2023, 16:00-17:00（Japan time） |
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Speaker | Masato Hayashi (Nagoya University/The Chinese University of Hong Kong) |

Title |
Iterative minimization algorithm on mixture family |

Place | Dept. of Mathematics, Faculty of Science Bldg., F404 |

Abstract |
Iterative minimization algorithms appear in various areas including machine learning, neural network, and information theory. The em algorithm is one of the famous iterative minimization algorithms in the former area, and Arimoto-Blahut algorithm is a typical iterative algorithm in the latter area. |

Date | July 4 (Tue.) 2023, 16:30-18:00（Japan time） |
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Speaker | Kazushi Kobayashi (Mie University) |

Title |
A gerby deformation of complex tori and the homological mirror symmetry |

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

Date | Jun 30 (Fri.) 2023, 17:15-18:15（After the Sugimoto Algebra Seminar） |
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Speaker | Rei Murakami (Tohoku University) |

Title |
J-equations on fiber spaces |

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

Date | Jun 16 (Fri.) 2023, 16:30-18:00（Japan time） |
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Speaker | Shota Hamanaka (Mitsubishi Electric Corporation) |

Title |
Some limit theorems for the total scalar curvature |

Place | Dept. of Mathematics, Faculty of Science Bldg., F404 |

Date | May 12 (Fri.) 2023, 16:30-18:00（Japan time） |
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Speaker | Tomás Otero (CITMAga - Universidade de Santiago de Compostela) |

Title |
Cohomogeneity one actions on symmetric spaces |

Place | Dept. of Mathematics, Faculty of Science Bldg., F404 |

Abstract |
An isometric action on a Riemannian manifold is of cohomogeneity one if the minimum codimension of its orbits is one or, equivalently, it has hypersurfaces as its regular orbits. While the classification of homogeneous hypersurfaces in real hyperbolic spaces follows from Cartan's classical work on isoparametric hypersurfaces, obtaining similar results for other symmetric spaces of noncompact type has proven to be difficult: For example, it was not until recently that the classification of homogeneous hypersurfaces on the quaternionic hyperbolic spaces was obtained. In noncompact symmetric spaces of higher rank, several structural results by J. Berndt and H. Tamaru allowed to obtain similar classifications, but only for certain irreducible spaces of rank two. In this talk I will report on the state of the classification of cohomogeneity one actions in symmetric spaces focusing on the case of symmetric spaces of noncompact type. Recently, in a joint work with J.Carlos Díaz-Ramos and Miguel Domínguez-Váquez we have proposed a generalized procedure for the classification of such actions on a given symmetric space of noncompact type. This allowed us to produce the first classification result of homogeneous hypersurfaces in a space of rank > 2, namely on the spaces SL(n,R)/SO(n). |

#### Differential Geometry Seminar (2023) Organizers

Name | Tel | |
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Hiroshi Tamaru | 06-6605-2615 | tamaru [at] omu.ac.jp |

Yoshinori Hashimoto | yhashimoto [at] omu.ac.jp | |

Hiroaki Ishida | hiroaki.ishida [at] omu.ac.jp | |

Shin Kato | 06-6605-2616 | shinkato [at] omu.ac.jp |

Takayuki Koike | tkoike [at] omu.ac.jp | |

Ushio Tanaka | utanaka [at] omu.ac.jp | |

Kaname Hashimoto | h-kaname [at] sci.osaka-cu.ac.jp |