# Hakata Workshop 2017

Last-modified: 2017-02-19 (日) 10:43:52 (518d)

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## Hakata Workshop 2017 †

**〜Discrete Mathematics and its Applications〜**

Our purpose of this meeting is giving an opportunity to make a speech and to communicate with researchers who study various fields not only Combinatorics.

Further information is available from the organizers below.

### Organizers †

- Yoshihiro Mizoguchi (Kyushu University),
- Takafumi Shibuta (Kyushu University),
- Tetsuji Taniguchi (Hiroshima Institute of Technology),
- Osamu Shimabukuro (Nagasaki University),
- Makoto Tagami ( Kyushu Institute of Technology),
- Hirotake Kurihara (Kitakyushu National College of Technology),
- Shuya Chiba (Kumamoto University).

### Supported by †

- Graduate School of Mathematics, Kyushu University
- JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.

### Date †

Thursday, February 23, 2017

### Location †

- Seminar Room I (2F) in Reference Eki Higashi Building. 1-16-14 Hakata-Eki-Higashi, Hakata-Ku, Fukuoka City, 812-0013 (see http://www.re-rental.com/ , Google maps )

### Program †

Speaker | Title | |
---|---|---|

9:18--9:20 | Opening (Tetsuji Taniguchi) | |

9:20--10:05 | Masatake Hirao(Aichi Prefectural University) | QMC designs on the sphere with determinantal point processes |

10:10--10:55 | Hirotake Kurihara(National Institute of Technology, Kitakyushu College) | Structures of association schemes on great antipodal sets of Hermitian symmetric spaces |

11:00--11:30 | Tadashi Aramaki(Kyushu University) | On the zeros of certain cusp forms related to the Eisenstein series for the Fricke groups of level 2 and 3 |

13:00--14:30 | Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop 2017) | |

15:00--15:45 | Taichi Kousaka(Kyushu University) | Some properties of highly-regular graphs |

15:55--16:40 | Takefumi Kondo(Kagoshima University) | Distortion of some finite graphs |

16:50--17:35 | Semin Oh(Pusan National University) | Demonstrations of finding finite groups all of whose symmetric fusion schemes are integral |

17:35--17:40 | Closing(Yoshihiro Mizoguchi) |

### List of Poster session speakers †

#### Software in Mathematics Demonstration Track in Hakata Workshop 2017 †

- Daniel GAINA (Japan Advanced Institute of Science and Technology (JAIST)) Constructor-based Inductive Theorem Prover (CITP)
- Semin Oh(Pusan National University) Demonstrations of finding finite groups all of whose symmetric fusion schemes are integral
- 平野友美 (九州大学大学院 数理学府数理学専攻) A mathematica module for 2-dimensional computer graphics
- 林美香 (九州工業大学情報工学府) 5頂点までの最小ユークリッド歪みについて
- 小泉和之 (横浜市立大学国際総合科学部) 客観的指標を用いた投手評価指標の提案
- Ye Yuan (九州大学大学院 数理学府数理学専攻) Efficient implementation of lattice-based encryption schemes on multiple platforms

### Abstract †

#### Masatake Hirao †

- Title: QMC designs on the sphere with determinantal point processes
- Abstract: The concept of a QMC(Quasi-Monte Carlo) design sequence was introduced by Brauchart et al (2014). In this talk we give a probabilistic generation of a sequence of QMC designs by using determinantal point processes (DPPs), which are used in a fermion model in quantum mechanics and also studied in probability theory. We show that spherical ensembles and harmonic ensembles, which are the typical types of DPPs on the sphere, give on average faster convergent sequences for Sobolev space on the sphere.

#### Tadashi Aramaki †

- Title: On the zeros of certain cusp forms related to the Eisenstein series for the Fricke groups of level 2 and 3.
- Abstract: The location of the zeros of Eisenstein series has been considered for a long time. It is known that the zeros of Eisenstein series for SL(2,Z) in the standard fundamental domain lie on the lower arc of it. In this talk, we will present several results for the location of the zeros of certain cusp forms related to the Eisenstein series for the Fricke groups of level 2 and 3.

#### Taichi Kousaka †

- Title: Some properties of highly-regular graphs
- Abstract: Classically, highly-regular graphs have been studied as a generalization of strongly-regular graphs. However, highly-regular graphs can also be regarded as a generalization of distance-regular graphs. From this view point, we study combinatorial and spectral aspects of highly-regular graphs. In this talk, as combinatorial results, we give two constructions of highly-regular graphs and some properties of CAM (collapsed adjacency matrix) of highly-regular graphs. Furthermore, we show that highly-regular graphs are spectrally-regular graphs.

#### Hirotake Kurihara †

- Title:Structures of association schemes on great antipodal sets of Hermitian symmetric spaces
- Abstract:
For a compact Hermitian symmetric space, there is a
**good**finite subset, which is called a great antipodal set. In this talk, we will show that each great antipodal set has a structure of an association scheme. This is a joint work with Takayuki Okuda (Hiroshima University).

#### Takefumi Kondo †

- Title:Distortion of some finite graphs
- Abstract: Using duality theory of semidefinite programming, Linial, London and Rabinovich obtained a characterization of the least possible distortion of embeddings of finite metric spaces into Euclidean space. I will describe how this result is applied to determine the Euclidean distortion of finite generalized polygons in a joint work with Toshimasa Kobayashi and then discuss other methods to compute the least distortion for embeddings into CAT(0) spaces.

#### Semin Oh †

- Title:Demonstrations of finding finite groups all of whose symmetric fusion schemes are integral
- Abstract:It is well-known that for a finite group
*G*the association scheme*G*can be obtained by its regular action. In this talk a finite group*G*is called desirable if for any symmetric fusion scheme of the association scheme of*G*is integral. Observing the one-to-one correspondence between the set of fusion schemes of the association scheme of*G*and the set of Schur rings over*G*, we will give demonstrations of finding finite desirable groups of small order by using GAP with COCO2p package.