MAS581. Topics in Mathematics: Combinatorics of Coxeter groups

  • Title. Combinatorics of Coxeter groups  (콕세터 군의 조합론)
  • Lecturer. Philippe Nadeau, CNRS & Université Claude Bernard Lyon 1, France
  • Date. 15(Fri.), 16(Sat.), 22(Fri.), 23(Sat.), May 2015
  • Time. 10h30 – 12h30 and 14h30 – 16h30
  • Venue. Room 2412, Building E6, Department of Mathematical Sciences, KAIST
  • Abstract. Coxeter groups are fundamental structures, given by generators and relations, which are closely related to transformation groups of quadratic spaces. In fact finite Coxeter groups are precisely the finite groups of isometries of an euclidean space which are generated by reflections. More generally, the repeated occurrence of Coxeter groups in various domains of algebra, geometry or combinatorics motivates their study.
    In these lectures, we will focus on the underlying combinatorial and enumerative 
    questions raised by these groups. We will start with the study of finite reflection groups, and give the classification result based on their Coxeter presentation. Then we will give the main properties of general Coxeter groups, based mainly from the point of view of words. In the last lectures, time permitting, we will study the specific combinatorics of affine Coxeter groups, and give an introduction to the active domain of noncrossing partitions associated to finite Coxeter groups.
Lecture 1. (May 15, 10h30) Motivating example: the symmetric group
Lecture 2. (May 15, 14h30) Finite reflection groups and their classification
Lecture 3. (May 16, 10h30) Coxeter groups and their geometric representation
Lecture 4. (May 16, 14h30) Basic properties of Coxeter groups
Lecture 5. (May 22, 10h30) Weak order and reduced decompositions
Lecture 6. (May 22, 14h30) Affine Coxeter groups
Lecture 7. (May 23, 10h30) Generalized noncrossing partitions
  • We are going to have a take-home exam after lectures.

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Participants

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Baek, Keonu KAIST Student 
Choi, Hojin KAIST Student 
Choi, Seung-Il  Sogang University Postdoc 
Cho, Minho KAIST Student 
Eom, Taehyun KAIST Student 
Fu, Shishuo Chongqing University, China / NIMS Professor 
Jang, Kyoungseok KAIST Student 
Jeong, Jongjeon KAIST Student 
Jung, Hongtaek KAIST Student 
Kang, Dongyeop KAIST Student 
Kim, Jang Soo Sungkyunkwan University Professor 
Kim, Yeonjin KAIST Postdoc 
Kim, Young Hun Sogang University Student 
Kwon, Yeong-Wook Sungkyunkwan University Student 
Lee, Sang-Jin  Konkuk University Professor 
Lee, Seunghun  KAIST Student 
Lin, Zhicong NIMS Postdoc 
Lyu, Yeonsig KAIST Student 
Nadeau, Philippe  Université Claude Bernard Lyon 1, France Researcher 
Ohlmann, Gaspard ENS, France / Sungkyunkwan University Student 
Oh, Young-Tak Sogang University Professor 
Oum, Sang-il KAIST Professor 
Park, Kyoungsuk  Ajou University Student 
Park, Minjae  KAIST Student 
Shin, Heesung Inha University / NIMS Professor 
Suh, Geewon KAIST Student 
Yun, Sum-mi  Sungkyunkwan University Student 
Zeng, Jiang Université Claude Bernard Lyon 1, France / NIMS Professor 
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Heesung Shin,
May 24, 2015, 12:34 AM
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Heesung Shin,
May 17, 2015, 5:57 PM