센터목표

 

본 연구센터는 표현론, 수론, 기하학에서 주요하게 제기되는 양자화된 대수적 구조의 연구를 통해 과거 독립적으로 연구되었던 분야들 간의 연관성을 구체적으로 규명하는 것을 목표로 하고 있다. 구체적으로 본 센터의 연구목표와 비전은 아래와 같다.

(1) 양자군과 헤케대수의 대수적, 산술적 구조 연구
(2) 사교다양체의 위상구조, 플로어이론, 양자대수 구조 연구
(3) 클러스터대수, 보형형식, 양자군, 사교기하학, 거울대칭의 연결고리를 설명하는 이론의 규명

 

모듈과 공간의 양자구조 연구센터는 과학기술정보통신부와 한국연구재단이 2020년부터 지원하는 선도연구센터 (SRC-Science Research Center) 입니다.

 

The research at the center for quantum structures in modules and spaces (QSMS) is centered around the quantized algebraic structures naturally arising from representation theory, number theory and geometry. Our aim is to investigate these algebraic structures and find concrete connections between them: the topics include

 

(1) algebraic and arithmetic structures of quantum groups and Hecke algebras

(2) topological and quantized algebraic structure of symplectic geometry, and Floer theory

(3) the connection between cluster algebras, modular forms, quantum groups, symplectic geometry, and mirror symmetry

 

The center for quantum structures in modules ans spaces is a Science Research Center (SRC) supported by the Ministry of Science and ICT (MSIT) and the National Research Foundation of Korea (NRF) since 2020.
 

 

구성원

 

제1그룹 모듈의 양자대수구조 (Quantum Algebraic Structures in Modules)

 

권재훈 Jae Hoon Kwon (Director) 

• 서울대학교(Seoul National University)
• Representation theory of Lie (super)algebras and their quantum groups    
• Contact:  jaehoonkw at snu dot ac dot kr
• Homepage:  https://sites.google.com/site/jaehoonkw/home

 

김명호 Myungho Kim

• 경희대학교(Kyung Hee University)
• Representation theory of quantum groups
• Contact:  mkim at khu dot ac dot kr  
• Homepage:  https://khu.elsevierpure.com/en/persons/myungho-kim/

 

박의용 Euiyong Park

• 서울시립대학교(University of Seoul)
• Representation theory for quantum Kac-Moody algebras, Categorification for quantum Kac-Moody Lie algebras and its applications
• Contact:  epark at uos dot ac dot kr
• https://sites.google.com/site/epark1024/

 

오병권 Byeong-Kweon Oh

• 서울대학교(Seoul National University)
• Number Theory
• Contact:  bkoh at snu dot ac dot kr
• http://www.math.snu.ac.kr/~bkoh/

 

유화종 Hwajong Yoo 

• 서울대학교(Seoul National University)
• Number theory, Arithmetic geometry
• Contact:  hwajong at snu dot ac dot kr
• https://sites.google.com/site/hwajong

 

 

제2그룹 공간의 양자대수구조 (Quantum Algebraic Structures in Spaces)

 

조철현 Cheol Hyun Cho (Deputy Director)

• 포항공과 대학교(POSTECH)
• Symplectic topology, Homological mirror symmetry, Stringy orbitfolds
• Contact:  chocheol at snu dot ac dot kr
• http://www.math.snu.ac.kr/~chocheol/

 

 강정수 Jungsoo Kang 

• 서울대학교(Seoul National University)
• Symplectic geometry, Floer theory
• Contact:  jungsoo dot kang at snu dot ac dot kr
• https://sites.google.com/site/jungsookangshome/

 

 김유식 Yoosik Kim 

• 부산대학교(Pusan National University)
• Symplectic topology, Floer theory, mirror symmetry, and integrable systems
• Contact:  yoosik (at) pusan (dot) ac (dot) kr
• https://sites.google.com/site/kimyoosik27/home

 

박종일 Jongil Park 

• 서울대학교(Seoul National University)
• Topology(Topology of 4-Manifolds)
• Contact:  jipark at snu dot ac dot kr
• http://www.math.snu.ac.kr/~jipark/

 

조윤형 Yunhyung Cho

• 성균관대학교(Sungkyunkwan University)
• Hamiltonian Lie group actions, Lagrangian Floer theory, Mirror symmetry, Cluster varieties, Toric degenerations
• Contact:  yunhyung at skku dot edu 
• https://sites.google.com/site/yhchomath/

 

홍한솔 Hansol Hong

• 연세대학교(Yonsei University)
• Symplectic Geometry, Lagrangian Floer theory, Homological mirror symmetry
• Contact:  hansolhong at yonsei dot ac dot kr
• https://sites.google.com/view/hansolhongmath/

 

 

선임연구원

박지훈 Jeehoon Park

• Number theory, arithmetic algebraic geometry, and their connections with physics
• Contact:  jpark.math at gmail dot com
• https://sites.google.com/view/jeehoonpark/home

 

최승일 Seung-Il Choi

• Combinatorial representation theory: Lie algebras, 0-Hecke algebras
• Contact:  ignatioschoi at snu dot ac dot kr

 

연수연구원

이석형 Seok Hyeong Lee

• Number Theory, Arithmetic Geometry
• Contact:  lshyeong at snu dot ac dot kr

 

유진주 Jinjoo Yoo

• Number theory, Function field, Algebraic coding theory
• Contact:  jinjooyoo at snu dot ac kr   
• sites.google.com/view/jinjooyoo

 

이동호 Dongho Lee

• Symplectic geometry, Symplectic dynamics, Three-body problem
• Contact:  tangled at snu dot ac kr   
• https://dhlee-math.github.io/

 

 

우리 센터와 함께한 사람들

김종명 Jongmyeong Kim

• (현) IBS-CGP Senior Research Fellow
• Homological mirror symmetry, Fukaya categories and categorical dynamics

• Contact: myeong (at) snu (dot) ac (dot) kr

• https://sites.google.com/view/thereisnoroyalroadtogeometry

 

배한울 Hanwool Bae

• (현) 전남대학교 조교수
• Symplectic Geometry, Lagrangian Floer theory, Homological mirror symmetry
• hanwoolb at gmail dot com
• https://sites.google.com/view/hanwoolbae

 

김영훈 Young-Hun Kim

• (현) 서울여자대학교 조교수
• Representation theory of 0-Hecke algebras, Symmetric functions and generalizations
• ykim,math at gmail dot com, yhkim at swu dot ac dot kr
• https://yhkimmath.wordpress.com/

 

실방 카펜티어  Sylvain Carpentier

• (현) 서울대학교 BK21FOUR 연구원
• Mathematical Physics, Algebraic structures of integrable systems
• sylvain dot carpentier23 at gmail.com
• https://sylvaincarpentier.github.io/

 

최학호 Hakho Choi

• (현) AI 스타트업

• Topology of smooth and symplectic 4-manifolds, Lefschetz fibration structure on symplectic 4-manifolds

• hakho85 at snu dot ac dot kr

 

조창연 Chang-Yeon Chough

• (현) 서강대학교 조교수
• (derived/spectral) algebraic geometry
• chough at sogang dot ac dot kr
• https://sites.google.com/view/chough

 

이동수 Dongsoo Lee 

• (현) KAIST 연구원 
• Low dimensional topology, knot concordance, knot Floer homology

 

장일승 Il-Seung Jang

• (현) 인천대학교 조교수
• representation theory of quantum groups, algebraic combinatorics
• ilseungjang at inu dort ac dot kr
• https://sites.google.com/view/isjang

 

 

직원

기유정  Yoo Jeong Ki  실장

• kyj0702 at snu dot ac dot kr

서명희  Seo Myeong Hee

• smh208 at snu dot ac dot kr