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入学希望の方 修了生の方 企業・研究者の方 教職員・学生 //--> Sitemap Access Japanese About GSISMessage from the DeanIntroduction to GSISGSIS guide bookOrganizationSNSJournal: Interdisciplinary Information SciencesContactsFacultyLaboratories by DepartmentComputer and Mathematical SciencesSystem Information SciencesHuman-Social Information SciencesApplied Information SciencesLaboratories by Specialized Subject GroupColaborative LaboratoriesPromotion OfficeAdmissionEntrance ExaminationCurriculum and Qualifications for ApplicationResearch StudentDormitoryFor StudentsSyllabus / Time table / Student HandbookNoticeInternational StudentsScholarshipDormitoryAdmission fee / Tuition fee waiverHandbook for International StudentsJapanese Language ProgramCounseling servicesEmergency InformationInternal Access Only Home Faculty Laboratories by Department Mathematical Structures I Computer and Mathematical Sciences Mathematical Structures I A01 Prof. Akihiro Munemasa     Assoc. Prof. BAO YUANYUAN Lab's Web page Bao Lab's Web page Keywordscombinatorics, algebraic graph theory, combinatorial designs, finite group theory, knots, 3-dim manifolds, quantum invariants, Heegaard Floer homology Research on mathematical theory with algebraic or discrete approach (1)  Algebraic combinatorics The theory of association schemes has been developed to unify the application of linear programming to coding theory and design theory by Delsarte in 1970&＃39;s. It generalizes the action of finite groups, and gives a framework for algebraic graph theory, algebraic coding theory and combinatorial design theory. In order to develop algebraic tools for these theories, we investigate applications of algebraic methods to combinatorics, mainly from graph spectra, finite groups, representation theory, linear algebra and optimization. (2) Codes and lattices A code is a subspace of a finite-dimensional vector space over a finite field. This seemingly simple concept has been widely used to study combinatorial problems using algebraic methods. Codes themselves can also be investigated from tools in number theory, modular forms in particular, via integral lattices. The class of self-dual codes is an interesting class of codes which give rise to unimodular lattices, and are related to the sphere packing problem and the theory of spherical designs. Moreover, some vertex operator algebras are constructed from codes and lattices. We investigate the problems of construction and classification of codes and lattices, and study their relations.   Research on knots and 3-dim manifolds I study knots and 3-dim manifolds,and my research topics include quantum invariants and Heegaard Floer homology. From a representation of a quantum group we can create an R- matrix, which is a solution to the Yang-Baxter equation. An R-matrix gives a matrix representation of braid group, and a quantum invariant is constructed in this way. Heegaard Floer homology is an invariant defined using techniques in symplectic geometry. I am interested in the topological applications and interpretations of these invariants. Two conjugacy classes of the symmetric group of degree 6 Yang-Baxter equation FacultyLaboratories by DepartmentComputer and Mathematical SciencesSystem Information SciencesHuman-Social Information SciencesApplied Information SciencesLaboratories by Specialized Subject GroupColaborative LaboratoriesPromotion Office GSIS: Graduate School of Information Sciences, Tohoku University 6-3-09 Aoba, Aramaki-aza Aoba-ku, Sendai, 980-8579, Japan Phone.+81-22-795-5813 Fax. +81-22-795-5815 Contacts is-www-admin,is.tohoku.ac.jp --> About GSIS Message from the DeanIntroduction to GSISGSIS guide bookOrganizationSNSJournal: Interdisciplinary Information SciencesContacts Faculty Laboratories by DepartmentComputer and Mathematical SciencesSystem Information SciencesHuman-Social Information SciencesApplied Information SciencesLaboratories by Specialized Subject GroupColaborative LaboratoriesPromotion Office Admission Entrance ExaminationCurriculum and Qualifications for ApplicationResearch StudentDormitory For Students Syllabus / Time table / Student HandbookNoticeInternational StudentsScholarshipDormitoryAdmission fee / Tuition fee waiverHandbook for International StudentsJapanese Language ProgramCounseling servicesEmergency InformationInternal Access Only About this Website Link © 2016 Graduate School of Information Sciences, Tohoku University About GSIS Message from the DeanIntroduction to GSISGSIS guide bookOrganizationSNSJournal: Interdisciplinary Information SciencesContacts Faculty Laboratories by DepartmentComputer and Mathematical SciencesSystem Information SciencesHuman-Social Information SciencesApplied Information SciencesLaboratories by Specialized Subject GroupColaborative LaboratoriesPromotion Office Admission Entrance ExaminationCurriculum and Qualifications for ApplicationResearch StudentDormitory For Students Syllabus / Time table / Student HandbookNoticeInternational StudentsScholarshipDormitoryAdmission fee / Tuition fee waiverHandbook for International StudentsJapanese Language ProgramCounseling servicesEmergency InformationInternal Access Only Sitemap Access Japanese no cache