Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program WSA36000 Specialized Education 多様幾何特論Ｄ タヨウキカトクロンデー Topics in Geometry D OKUDA TAKAYUKI,ISHIHARA KAI,FUJIMORI SHOICHI オクダ　タカユキ,イシハラ　カイ,フジモリ　ショウイチ Higashi-Hiroshima 1st-Year,  Second Semester,  3Term (3T) Weds5-6,Fri7-8：Online Lecture 2.0 B : Japanese／English 4 : Undergraduate Advanced 25 : Science and Technology 01 : Mathematics/Statistics Homogeneous spaces, Coding theory, Representation theory, Fourier analysis The purpose is to understand applications of Fourier analysis on coding theory on homogeneous spaces. lesson1 Introductionlesson2 Coding theory on metric spaceslesson3 Error correcting codeslesson4 Kissing number problemslesson5 Compact homogeneous spaceslesson6 Inner-distributions of point arrangements on compact homogeneous spaceslesson7 Haar measures on compact groupslesson8 Linear representations of compact groupslesson9 Intertwining operatorslesson10 Compact Gelfand pairs and commutative compact homogeneous spaceslesson11 Peter--Weyl's theorem on commutative spaces.lesson12 Spherical Fourier analysis on commutative spaces.lesson13 An application of Spherical Fourier analysis on coding theory on commutative spaceslesson14 For non-commutative spaceslesson15 SummaryHomework will be assigned in the lecture. No textbook. Reference books:Bannai, E., Bannai, E., Ito, T., & Tanaka, R. (2021). Algebraic combinatorics (Vol. 5). Walter de Gruyter GmbH & Co KG.Toshiyuki Kobayashi (小林俊行), Toshio Oshima (大島利雄), Lie group and Representation theory (in Japanese: リー群と表現論), Iwanami, 2005 In each lecture, some easy computations and proofs will be omitted.It is needed to check them by your hand.Asking questions to the lecturer is always welcome. Evaluation will be based on homework assignments. Please fill in the class improvement questionnaire which is carried out on all classes.Instructors will reflect on your feedback and utilize the information for improving their teaching.
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