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Hakata Workshop 2015 の履歴(No.4)


Hakata Workshop 2015

~Discrete Mathematics and its Applications~

 

Our purpose of this meeting is giving an opportunity to make a speech and to commuticate with reserchers who study verious fields not only Combinatorics.

Further information is available from the organizers below.

Organizers

  • Yoshihiro Mizoguchi (Kyushu University),
  • Hayato Waki (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

Date

Sunday, February 15, 2015

Location

Program

SpeakerTitle
9:48--9:50Opening (Tetsuji Taniguchi)
9:50--10:35Osamu Ikawa(Kyoto Institute of Technology)Symmetric triad -a generalization of root system-
10:45--11:30Hiroyuki Tasaki(University of Tsukuba)Antipodal sets in oriented real Grassmann manifolds
13:00--14:30 Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop 2015)
14:50--15:35Masanori Sawa (Kobe University)On a countable uniform hypergraph with generic structure and its finite-combinatorial aspect
15:45--16:30Mami Okiyoshi(Hiroshima University)Generating functions of Box and Ball System
16:40--17:25Kazunori Sakurama(Tottori University)TBA
17:25--17:30Closing(Yoshihiro Mizoguchi)

List of Poster session speakers

Software in Mathematics Demonstration Track in Hakata Workshop 2015

Abstract

Osamu Ikawa

  • Title: Symmetric triad -a generalization of root system-
  • Abstract: A root system was defined by a finite subset of a finite dimensional vector space with an inner product that satisfies a certain condition. A root system with multiplicities is a superstructure of a root system, that is a useful tool if we consider the orbit of an isotropy group of a symmetric space. In fact the orbit space is described in terms of a root system with multiplicities which is obtained by the symmetric space. Further the condition the orbit to be regular, singular, minimal and totally geodesic is also described in terms of a root system with multiplicities. A Hermann action is an isometric action on a symmetric space, which is a generalization of isotropy action on a symmetric space and inherits nice properties such as hyperpolarity and variational completeness. If we generalize the notion of a root system with multiplicities to that of a symmetric triad with multiplicities, then it is useful when we consider the orbit of a Hermann action. In fact the orbit space of a Hermann action is described in terms of a symmetric triad with multiplicities which is obtained by the Hermann action. Further the condition the orbit to be regular, singular, minimal and totally geodesic is also described in terms of a symmetric triad with multiplicities.

Hiroyuki Tasaki

  • Title:Antipodal sets in oriented real Grassmann manifolds
  • Abstract: Antipodal sets in a Riemannian symmetric space is defined in a geometric way by the use of geodesic symmetries. The oriented real Grassmann manifold is a Reimannian symmetric space and antipodal sets in it correspond to certain combinatorial objects. In the case where the rank of the oriented real Grassmann manifold is less than five we give the classification of antipodal sets in it. In the case where the rank is equal to five we determine antipodal sets of maximal cardinality. We mention a recent result of Frankl and Tokushige in the case of higher rank.

Masanori Sawa

  • Title:On a countable uniform hypergraph with generic structure and its finite-combinatorial aspect
  • Abstract: In this talk we consider a sequence of finite hypergraphs, each characterized by the so-called pre-dimension function, and provide a countable graph with generic structure as well as model completeness. The aim of this talk is to inform Hrushovski's amalgamation to people in finite combinatorics, rather than making a new mathematics.

Mami Okiyoshi

  • Title:Generating functions of Box and Ball System
  • Abstract: In 1990, Takashi-Satsuma introduced a discrete soliton system called Box and Ball System (BBS). We define generating functions of BBS and ask if they are rational functions. When the number of balls is finite, we show that the generating function is a rational function, which essentially follows from the result of Takahashi-Satsuma. When there are infinitely many balls, we conjecture that the generating function is rational if and only if the BBS is semi-periodic. We prove the conjecture in special cases. We also study the generating function of the BBS with a limited cart, including semi-periodic cases.

Kazunori Sakurama

  • Title:TBA
  • Abstract: TBA