# Differential Geometry Seminar (2024)

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 (2024) Talks

Date | December 16 (Mon.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Michiaki Inaba (Nara Women's University) |

Title |
TBA |

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

Abstract |
TBA |

Date | December 6 (Fri.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Yasufumi Nitta (Tokyo University of Science) |

Title |
TBA |

Place | Faculty of Science Bldg., E211 |

Abstract |
TBA |

Date | November 27 (Wed.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | David O’Connell (Okinawa Institute of Science and Technology) |

Title |
TBA |

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

Abstract |
TBA |

Date | September 9 (Mon.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Wolfram Bauer (Leibniz Universität Hannover) |

Title |
Subriemannian geometry and spectral analysis |

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

Abstract |
A regular subriemannian manifold M carries a geometric hypoelliptic operator, the intrinsic sublaplacian. Due to a degeneracy of its symbol, geometric and analytic e ects can be observed in the study of this operator, which have no counterpart in Riemannian geometry. During the last decades inverse spectral problems in subriemannian geometry have been studied by various authors. Typical approaches are based on the analysis of the induced subriemannian heat or wave equation. In this talk we survey some results in subriemannian geometry. In particular, we address the spectral theory of the sublaplacian in the case of certain compact nilmanifolds or, more generally, for H-type foliations. This talk is based on joint work with K. Furutani, C. Iwasaki, A. Laaroussi, I. Markina and S. Vega-Molino. |

Date | July 19 (Fri.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Wafaa Batat (Ecole Nationale Polytechnique d'Oran Maurice Audin) |

Title |
Homogeneous Structures on Three- and Four-dimensional Lie groups |

Place | Dept. of Mathematics, Faculty of Science Bldg., F405 |

Abstract |
In this talk, we will introduce the notion of homogeneous pseudo-Riemannian structures and demonstrate how to establish homogeneity and natural reductiveness of 3- and 4-dimensional Lie groups through a tensor satisfying certain geometric partial differential equations involving the metric and the curvature of a given manifold. These equations are known as Ambrose-Singer equations. We will begin by examining homogeneous structures on three-dimensional unimodular and non-unimodular Lie groups, proving the existence of homogeneous Lorentzian structures that differ from the canonical ones without being naturally reductive, a phenomenon with no Riemannian counterpart. Using these homogeneous structures, we will show how to classify naturally reductive 3-dimensional Lorentzian manifolds. Our focus will then shift to the geometric properties of four-dimensional nilpotent Lie groups endowed with a family of non-flat left-invariant Lorentzian metrics. We will conduct a comprehensive classification of homogeneous structures for each metric and meticulously examine the distinctive properties characterizing each structure. Additionally, we will provide a specific example demonstrating the presence of a naturally reductive, non-flat, left-invariant Lorentzian metric on the 2-nilpotent Lie group, where the center exhibits degeneracy. Furthermore, we will establish the existence of a non-canonical homogeneous structure. As an application, we will demonstrate the existence of naturally reductive left-invariant Lorentzian metrics on the four-dimensional 3-nilpotent Lie group. |

Date | July 5 (Fri.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Christopher Mahadeo (University of Illinois at Chicago) |

Title |
Topological recursion and twisted Higgs bundles |

Place | Dept. of Mathematics, Faculty of Science Bldg., F405 |

Abstract |
Prior works relating meromorphic Higgs bundles to topological recursion have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. I will discuss some recent work where we define a "twisted topological recursion" on the spectral curve of a twisted Higgs bundle, and show that the g=0 components of the recursion compute the Taylor expansion of the period matrix of the spectral curve, mirroring a result of for ordinary Higgs bundles and topological recursion. I will also discuss some current work relating topological recursion to a new viewpoint of quantization of Higgs bundles. |

Date | May 24 (Fri.) 2024, 16:45-18:15（Japan time) |
---|---|

Speaker | Yasuhiko Asao (Fukuoka University) |

Title |
Homology of metric spaces |

Place | Faculty of Science Bldg., E101 |

#### Differential Geometry Seminar (2024) Organizers

Name | Tel | |
---|---|---|

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 |